giải pt
a) \(\sqrt{2x^2+5x+2}-2\sqrt{2x^2+5x-6}=0\)
b) \(\sqrt[5]{\frac{16x}{x-1}}+\sqrt[5]{\frac{x-1}{16x}}=\frac{5}{2}\)
c) \(\sqrt{6x^2-12x+7}+2x=x^2\)
d) \(x\left(x+1\right)-\sqrt{x^2+x+4}+2=0\)
e) \(\sqrt{3x^2+6x+4}=2-2x-x^2\)
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28 tháng 11 2019 lúc 23:30
Giải các pt sau:
a) sqrt{x+8}+frac{9x}{sqrt{x+8}}-6sqrt{x}0
b) x^4-2x^3+sqrt{2x^3+x^2+2}-20
c) 3xsqrt[3]{x+7}left(x+sqrt[3]{x+7}right)7x^3+12x^2+5x-6
d) 4x^2+left(8x-4right)sqrt{x}-13x+2sqrt{2x^2+5x-3}
e) 16x^2+19x+7+4sqrt{-3x^2+5x+2}left(8x+2right)left(sqrt{2-x}+2sqrt{3x+1}right)
f) left(5x+8right)sqrt{2x-1}+7xsqrt{x+3}9x+8-left(x+26right)sqrt{x-1}
g) sqrt[3]{3x+1}+sqrt[3]{5-x}+sqrt[3]{2x-9}-sqrt[3]{4x-3}0
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Giải các pt sau:
a) \(\sqrt{x+8}+\frac{9x}{\sqrt{x+8}}-6\sqrt{x}=0\)
b) \(x^4-2x^3+\sqrt{2x^3+x^2+2}-2=0\)
c) \(3x\sqrt[3]{x+7}\left(x+\sqrt[3]{x+7}\right)=7x^3+12x^2+5x-6\)
d) \(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}\)
e) \(16x^2+19x+7+4\sqrt{-3x^2+5x+2}=\left(8x+2\right)\left(\sqrt{2-x}+2\sqrt{3x+1}\right)\)
f) \(\left(5x+8\right)\sqrt{2x-1}+7x\sqrt{x+3}=9x+8-\left(x+26\right)\sqrt{x-1}\)
g) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)
Hung nguyen, Trần Thanh Phương, Sky SơnTùng, @tth_new, @Nguyễn Việt Lâm, @Akai Haruma, @No choice teen
help me, pleaseee
Cần gấp lắm ạ!
2. Giải PT:
a) \(\frac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}.\)
b) \(\sqrt{4x-20}+3\sqrt{\frac{x-5}{9}}-\frac{1}{3}\sqrt{9x-45}=4.\)
c) \(2x-x^2+\sqrt{6x^2-12x+7}=0.\)
d) \(\left(x+1\right)\left(x+4\right)-3\sqrt{x^2+5x+2}=6.\)
\(a,\frac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}\)\(ĐKXĐ:x\ge-\frac{5}{7}\)
\(\Leftrightarrow9x-7=7x+5\)
\(\Leftrightarrow9x-7x=5+7\)
\(\Leftrightarrow2x=12\)
\(\Leftrightarrow x=6\)
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\(b,\sqrt{4x-20}+3\sqrt{\frac{x-5}{9}}-\frac{1}{3}\sqrt{9x-45}=4\)
\(\Leftrightarrow\sqrt{4\left(x-5\right)}+3.\frac{\sqrt{x-5}}{\sqrt{9}}-\frac{1}{3}\sqrt{9\left(x-5\right)}=4\)
\(\Leftrightarrow2\sqrt{x-5}+\sqrt{x-5}-\sqrt{x-5}=4\)
\(\Leftrightarrow\sqrt{x-5}\left(2+1-1\right)=4\)
\(\Leftrightarrow2\sqrt{x-5}=4\)
\(\Leftrightarrow\sqrt{x-5}=2\)
\(\Leftrightarrow x-5=4\)
\(\Leftrightarrow x=9\)
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26 tháng 10 2019 lúc 22:59
giải pt
a) 3sqrt{x}+frac{3}{2sqrt{x}}2x+frac{1}{2x}-7
b) 5sqrt{x}+frac{5}{2sqrt{x}}2x+frac{1}{2x}+4
c) sqrt{2x^2+8x+5}+sqrt{2x^2-4x+5}6sqrt{x}
d) x+1+sqrt{x^2-4x+1}3sqrt{x}
e) x^2+2xsqrt{x-frac{1}{x}}3x+1
f) x^2-6x+xsqrt{frac{x^2-6}{x}}-60
g) frac{3x^2}{3+sqrt{x}}+6+2sqrt{x}5x
h) frac{x^2}{4-3sqrt{x}}+83left(x+2sqrt{x}right)
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giải pt
a) \(3\sqrt{x}+\frac{3}{2\sqrt{x}}=2x+\frac{1}{2x}-7\)
b) \(5\sqrt{x}+\frac{5}{2\sqrt{x}}=2x+\frac{1}{2x}+4\)
c) \(\sqrt{2x^2+8x+5}+\sqrt{2x^2-4x+5}=6\sqrt{x}\)
d) \(x+1+\sqrt{x^2-4x+1}=3\sqrt{x}\)
e) \(x^2+2x\sqrt{x-\frac{1}{x}}=3x+1\)
f) \(x^2-6x+x\sqrt{\frac{x^2-6}{x}}-6=0\)
g) \(\frac{3x^2}{3+\sqrt{x}}+6+2\sqrt{x}=5x\)
h) \(\frac{x^2}{4-3\sqrt{x}}+8=3\left(x+2\sqrt{x}\right)\)
a/ ĐKXĐ: ...
\(\Leftrightarrow3\left(\sqrt{x}+\frac{1}{2\sqrt{x}}\right)=2\left(x+\frac{1}{4x}\right)-7\)
Đặt \(\sqrt{x}+\frac{1}{2\sqrt{x}}=a>0\Rightarrow a^2=x+\frac{1}{4x}+1\)
\(\Rightarrow x+\frac{1}{4x}=a^2-1\)
Pt trở thành:
\(3a=2\left(a^2-1\right)-7\)
\(\Leftrightarrow2a^2-3a-9=9\Rightarrow\left[{}\begin{matrix}a=3\\a=-\frac{3}{2}\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{x}+\frac{1}{2\sqrt{x}}=3\)
\(\Leftrightarrow2x-6\sqrt{x}+1=0\)
\(\Rightarrow\sqrt{x}=\frac{3+\sqrt{7}}{2}\Rightarrow x=\frac{8+3\sqrt{7}}{2}\)
b/ ĐKXĐ:
\(\Leftrightarrow5\left(\sqrt{x}+\frac{1}{2\sqrt{x}}\right)=2\left(x+\frac{1}{4x}\right)+4\)
Đặt \(\sqrt{x}+\frac{1}{2\sqrt{x}}=a>0\Rightarrow x+\frac{1}{4x}=a^2-1\)
\(\Rightarrow5a=2\left(a^2-1\right)+4\Leftrightarrow2a^2-5a+2=0\)
\(\Rightarrow\left[{}\begin{matrix}a=2\\a=\frac{1}{2}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\sqrt{x}+\frac{1}{2\sqrt{x}}=2\\\sqrt{x}+\frac{1}{2\sqrt{x}}=\frac{1}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x-4\sqrt{x}+1=0\\2x-\sqrt{x}+1=0\left(vn\right)\end{matrix}\right.\)
c/ ĐKXĐ: ...
\(\Leftrightarrow\sqrt{2x^2+8x+5}-4\sqrt{x}+\sqrt{2x^2-4x+5}-2\sqrt{x}=0\)
\(\Leftrightarrow\frac{2x^2-8x+5}{\sqrt{2x^2+8x+5}+4\sqrt{x}}+\frac{2x^2-8x+5}{\sqrt{2x^2-4x+5}+2\sqrt{x}}=0\)
\(\Leftrightarrow\left(2x^2-8x+5\right)\left(\frac{1}{\sqrt{2x^2+8x+5}+4\sqrt{x}}+\frac{1}{\sqrt{2x^2-4x+5}+2\sqrt{x}}\right)=0\)
\(\Leftrightarrow2x^2-8x+5=0\)
d/ ĐKXĐ: ...
\(\Leftrightarrow x+1-\frac{15}{6}\sqrt{x}+\sqrt{x^2-4x+1}-\frac{1}{2}\sqrt{x}=0\)
\(\Leftrightarrow\frac{x^2-\frac{17}{4}x+1}{\left(x+1\right)^2+\frac{15}{6}\sqrt{x}}+\frac{x^2-\frac{17}{4}x+1}{\sqrt{x^2-4x+1}+\frac{1}{2}\sqrt{x}}=0\)
\(\Leftrightarrow\left(x^2-\frac{17}{4}x+1\right)\left(\frac{1}{\left(x+1\right)^2+\frac{15}{6}\sqrt{x}}+\frac{1}{\sqrt{x^2-4x+1}+\frac{1}{2}\sqrt{x}}\right)=0\)
\(\Leftrightarrow x^2-\frac{17}{4}x+1=0\)
\(\Leftrightarrow4x^2-17x+4=0\)
e/ ĐKXĐ: ...
\(\Leftrightarrow x^2-1+2x\sqrt{\frac{x^2-1}{x}}=3x\)
Nhận thấy \(x=0\) không phải nghiệm, pt tương đương:
\(\frac{x^2-1}{x}+2\sqrt{\frac{x^2-1}{x}}=3\)
Đặt \(\sqrt{\frac{x^2-1}{x}}=a\ge0\)
\(a^2+2a=3\Leftrightarrow a^2+2a-3=0\Rightarrow\left[{}\begin{matrix}a=1\\a=-3\left(l\right)\end{matrix}\right.\)
\(\Leftrightarrow\sqrt{\frac{x^2-1}{x}}=1\Leftrightarrow x^2-1=x\Leftrightarrow x^2-x-1=0\)
f/ ĐKXĐ: ...
\(\Leftrightarrow x^2-6+x\sqrt{\frac{x^2-6}{x}}-6x=0\)
Nhận thấy \(x=0\) ko phải nghiệm, pt tương đương:
\(\frac{x^2-6}{x}+\sqrt{\frac{x^2-6}{x}}-6=0\)
Đặt \(\sqrt{\frac{x^2-6}{x}}=a\ge0\)
\(a^2+a-6=0\Rightarrow\left[{}\begin{matrix}a=2\\a=-3\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{\frac{x^2-6}{x}}=2\Leftrightarrow x^2-4x-6=0\)
Xem thêm câu trả lời
giải pt :
a, (x+5)(2-x)=3\(\sqrt{x^2+3x}\)
b, \(\sqrt[3]{\dfrac{2x}{x+1}}+\sqrt[3]{\dfrac{1}{2}+\dfrac{1}{2x}}=2\)
c,\(\sqrt[5]{\dfrac{16x}{x-1}}+\sqrt[5]{\dfrac{x-1}{16x}}=\dfrac{5}{2}\)
d, \(\sqrt{5x^2+10x+1}=7-2x-x^2\)
e, \(\sqrt{2x^2+4x+1}=1-2x-x^2\)
27 tháng 10 2019 lúc 12:34
giải pt
a) \(\sqrt[3]{x+6}+\sqrt{x-1}=x^2-1\)
b) \(\sqrt[3]{x-9}+2x^2+3x=\sqrt{5x-1}+1\)
c) \(\sqrt{3x+1}-\sqrt{6-x}+3x^2-14x-8=0\)
d) \(\sqrt{x+1}-2\sqrt{4-x}=\frac{5\left(x-3\right)}{\sqrt{2x^2+18}}\)
e) \(x^3+5x^2+6x=\left(x+2\right)\left(\sqrt{2x+2}+\sqrt{5-x}\right)\)
(Nghi binh 20/09)Giải các phương trình sau:a)32x^4-80x^3+50x^2+4x-3-4sqrt{x-1}0b) sqrt{5x^3-12x^2+12x-7}frac{x^2}{2}+2x-3c)sqrt{2x^2-16x+41}+sqrt{3x^2-24x+64}7d)x+sqrt{2x-3}1+sqrt{x-1}+sqrt{x^2-3x+3}e) left(2x-1right)sqrt{x^2+1}x^2+4x-5f)sqrt{8+sqrt{x}}+sqrt{5-sqrt{x}}5g)2left(x^2+2x+3right)5sqrt{x^3+3x^2+3x+2}h)sqrt[3]{81x-8}x^3-2x^2+frac{4}{3}x-2i)sqrt{xleft(x+1right)}+sqrt{xleft(x+2right)}sqrt{xleft(x-3right)}
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(Nghi binh 20/09)
Giải các phương trình sau:
a)\(32x^4-80x^3+50x^2+4x-3-4\sqrt{x-1}=0\)
b) \(\sqrt{5x^3-12x^2+12x-7}=\frac{x^2}{2}+2x-3\)
c)\(\sqrt{2x^2-16x+41}+\sqrt{3x^2-24x+64}=7\)
d)\(x+\sqrt{2x-3}=1+\sqrt{x-1}+\sqrt{x^2-3x+3}\)
e) \(\left(2x-1\right)\sqrt{x^2+1}=x^2+4x-5\)
f)\(\sqrt{8+\sqrt{x}}+\sqrt{5-\sqrt{x}}=5\)
g)\(2\left(x^2+2x+3\right)=5\sqrt{x^3+3x^2+3x+2}\)
h)\(\sqrt[3]{81x-8}=x^3-2x^2+\frac{4}{3}x-2\)
i)\(\sqrt{x\left(x+1\right)}+\sqrt{x\left(x+2\right)}=\sqrt{x\left(x-3\right)}\)
\(\sqrt{2x^2-16x+41}+\sqrt{3x^2-24x+64}=7\)
Ta đánh giá vế phải \(\sqrt{2x^2-16x+41}+\sqrt{3x^2-24x+64}=\sqrt{2\left(x-4\right)^2+9}+\sqrt{3\left(x-4\right)^2+16}\ge\sqrt{9}+\sqrt{16}=3+4=7\)(Do \(\left(x-4\right)^2\ge0\forall x\))
Như vậy, để \(\sqrt{2x^2-16x+41}+\sqrt{3x^2-24x+64}=7\)(hay dấu "=" xảy ra) thì \(\left(x-4\right)^2=0\)hay x = 4
Vậy nghiệm duy nhất của phương trình là 4
f, \(\sqrt{8+\sqrt{x}}+\sqrt{5-\sqrt{x}}=5\left(đk:25\ge x\ge0\right)\)
\(< =>\sqrt{8+\sqrt{x}}-\sqrt{9}+\sqrt{5-\sqrt{x}}-\sqrt{4}=0\)
\(< =>\frac{8+\sqrt{x}-9}{\sqrt{8+\sqrt{x}}+\sqrt{9}}+\frac{5-\sqrt{x}-4}{\sqrt{5-\sqrt{x}}+\sqrt{4}}=0\)
\(< =>\frac{\sqrt{x}-1}{\sqrt{8+\sqrt{x}}+\sqrt{9}}-\frac{\sqrt{x}-1}{\sqrt{5-\sqrt{x}}+\sqrt{4}}=0\)
\(< =>\left(\sqrt{x}-1\right)\left(\frac{1}{\sqrt{8+\sqrt{x}}+\sqrt{9}}-\frac{1}{\sqrt{5-\sqrt{x}}+\sqrt{4}}\right)=0\)
\(< =>x=1\)( dùng đk đánh giá cái ngoặc to nhé vì nó vô nghiệm )
giải pt:
a,\(\left(13-4x\right)\sqrt{2x-3}+\left(4x-3\right)\sqrt{5-2x}=2+8\sqrt{-4x^2+16x-15}\)
b,\(\left(9x-2\right)\sqrt{3x-1}+\left(10-9x\right)\sqrt{3-3x}-4\sqrt{-9x^2+12x-3}=4\)
c, \(\left(6x-5\right)\sqrt{x+1}-\left(6x+2\right)\sqrt{x-1}+4\sqrt{x^2-1}=4x-3\)
22 tháng 10 2019 lúc 17:12
Giải pt
a) 2x^2+sqrt{x^2-5x-6}10x+15
b) 5sqrt{3x^2-4x-2}-6x^2+8x+70
c) x^2+sqrt{2x^2+4x+3}6-2x
d) 2sqrt{frac{3x-1}{x}}frac{x}{3x-1}+1
e) sqrt{frac{24x-4}{x}}frac{x}{6x-1}+1
f) sqrt{frac{2x-1}{x}}+1+sqrt{frac{x}{2x-1}}frac{3x}{2x-1}
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Giải pt
a) \(2x^2+\sqrt{x^2-5x-6}=10x+15\)
b) \(5\sqrt{3x^2-4x-2}-6x^2+8x+7=0\)
c) \(x^2+\sqrt{2x^2+4x+3}=6-2x\)
d) \(2\sqrt{\frac{3x-1}{x}}=\frac{x}{3x-1}+1\)
e) \(\sqrt{\frac{24x-4}{x}}=\frac{x}{6x-1}+1\)
f) \(\sqrt{\frac{2x-1}{x}}+1+\sqrt{\frac{x}{2x-1}}=\frac{3x}{2x-1}\)
a/ ĐKXĐ: ...
\(\Leftrightarrow2\left(x^2-5x-6\right)+\sqrt{x^2-5x-6}-3=0\)
Đặt \(\sqrt{x^2-5x-6}=a\ge0\)
\(2a^2+a-3=0\Rightarrow\left[{}\begin{matrix}a=1\\a=-\frac{3}{2}\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{x^2-5x-6}=1\Leftrightarrow x^2-5x-7=0\)
b/ ĐKXĐ: ...
\(\Leftrightarrow5\sqrt{3x^2-4x-2}-2\left(3x^2-4x-2\right)+3=0\)
Đặt \(\sqrt{3x^2-4x-2}=a\ge0\)
\(-2a^2+5a+3=0\) \(\Rightarrow\left[{}\begin{matrix}a=3\\a=-\frac{1}{2}\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{3x^2-4x-2}=3\Leftrightarrow3x^2-4x-11=0\)
c/ \(\Leftrightarrow x^2+2x-6+\sqrt{2x^2+4x+3}=0\)
Đặt \(\sqrt{2x^2+4x+3}=a>0\Rightarrow x^2+2x=\frac{a^2-3}{2}\)
\(\frac{a^2-3}{2}-6+a=0\Leftrightarrow a^2+2a-15=0\Rightarrow\left[{}\begin{matrix}x=3\\x=-5\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{2x^2+4x+3}=3\Leftrightarrow2x^2+4x-6=0\)
d/ ĐKXĐ: ...
Đặt \(\sqrt{\frac{3x-1}{x}}=a>0\)
\(2a=\frac{1}{a^2}+1\Leftrightarrow2a^3-a^2-1=0\)
\(\Leftrightarrow\left(a-1\right)\left(2a^2+a+1\right)=0\)
\(\Rightarrow a=1\Rightarrow\sqrt{\frac{3x-1}{x}}=1\Leftrightarrow3x-1=x\)
e/ĐKXĐ: ...
\(\Leftrightarrow2\sqrt{\frac{6x-1}{x}}=\frac{x}{6x-1}+1\)
Đặt \(\sqrt{\frac{6x-1}{x}}=a>0\)
\(2a=\frac{1}{a^2}+1\Leftrightarrow2a^3-a^2-1=0\Leftrightarrow\left(a-1\right)\left(2a^2+a+1\right)=0\)
\(\Rightarrow a=1\Rightarrow\sqrt{\frac{6x-1}{x}}=1\Rightarrow6x-1=x\)
f/ ĐKXĐ: ...
Đặt \(\sqrt{\frac{x}{2x-1}}=a>0\)
\(\frac{1}{a}+1+a=3a^2\)
\(\Leftrightarrow3a^3-a^2-a-1=0\)
\(\Leftrightarrow\left(a-1\right)\left(3a^2+2a+1\right)=0\)
\(\Leftrightarrow a=1\Rightarrow\sqrt{\frac{x}{2x-1}}=1\Rightarrow x=2x-1\)
Giải phương trình sau:
a) \(\sqrt{4x+20}-3\sqrt{5+x}+\dfrac{4}{3}\sqrt{9x+45}=6\)
b) \(\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{9x-9}+24\sqrt{\dfrac{x-1}{64}}=-17\)
c) \(2x-x^2+\sqrt{6x^2-12x+7}=0\)
d) \(\left(x+1\right)\left(x+4\right)-3\sqrt{x^2+5x+2}=6\)
a: Ta có: \(\sqrt{4x+20}-3\sqrt{x+5}+\dfrac{4}{3}\sqrt{9x+45}=6\)
\(\Leftrightarrow2\sqrt{x+5}-3\sqrt{x+5}+4\sqrt{x+5}=6\)
\(\Leftrightarrow3\sqrt{x+5}=6\)
\(\Leftrightarrow x+5=4\)
hay x=-1
b: Ta có: \(\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{9x-9}+24\sqrt{\dfrac{x-1}{64}}=-17\)
\(\Leftrightarrow\dfrac{1}{2}\sqrt{x-1}-\dfrac{9}{2}\sqrt{x-1}+3\sqrt{x-1}=-17\)
\(\Leftrightarrow\sqrt{x-1}=17\)
\(\Leftrightarrow x-1=289\)
hay x=290
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