a) Điều kiện $x \ge -5$. Đặt $\sqrt{x+5}=a$ thì $x=a^2-5$. Thay vào ta có $$\begin{array}{l} (a^2-5)^2-7(a^2-5)=6a-30 \\ \Leftrightarrow a^4-17a^2-6a+90=0 \Leftrightarrow (a^2+6a+10)(a-3)^2=0 \end{array}$$
Vậy $a=3 \Leftrightarrow \boxed{ x= 4}$.
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) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)
a)\(\sqrt{1-x}\left(x-3x^2\right)=x^3-3x^2+2x+6\)
b)\(x^2+x+12\sqrt{x+1}=36\)
c)\(3x-1+\frac{x-1}{4x}=\sqrt{3x+1}\)
d)\(\sqrt{x^2+12}-3x=\sqrt{x^2+5}-5\)
e)\(4x^2+12+\sqrt{x-1}=4\left(x\sqrt{5x-1}+\sqrt{9-5x}\right)\)
f)\(4x^3-25x^2+43x+x\sqrt{3x-2}=22+\sqrt{3x-2}\)
g)\(2\left(x+1\right)\sqrt{x}+\sqrt{3\left(2x^3+5x^2+4x+1\right)}=5x^3-3x^2+8\)
h)\(\sqrt{x^2+12}-\sqrt{x^2+5}=3x-5\)
i)\(\sqrt{1-3x}-\sqrt[3]{3x-1}=\left|6x-2\right|\)
k)\(\sqrt{2x^3+3x^2-1}=2x^2+2x-x^3-1\)
l)\(\sqrt{x^2+x-2}+x^2=\sqrt{2\left(x-1\right)}+1\)
Giải phương trình:
1, \(3x^2+6x-3=\sqrt{\dfrac{x+7}{3}}\) (2 cách khác nhau )
2, \(\left(\sqrt{3x+1}-\sqrt{x-2}\right)\left(\sqrt{3x^2+7x+2}+4\right)=4x-2\)
3, \(\sqrt{-3x-1}+\sqrt{9x^2+9x+3}=-9x^2-6x\)
4, \(\sqrt{x^2+x-6}+3\sqrt{x-1}=\sqrt{5x^2-1}\)
5, \(\left(\sqrt{x+4}+2\right)\left(x+2\sqrt{x-5}+1\right)=6x\)
6, \(\sqrt{5-x^4}-\sqrt[3]{3x^2-2}=1\)
7, \(3x^2+11+\sqrt{x-2}+\sqrt{2x+3}=14x\)
8, \(\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-7}}}}=7\)
9, \(\sqrt{2x^2-1}+3x\sqrt{x^2-1}=3x^3+2x^2-9x-7\) ( với \(x>0\) )
Gpt : a) \(\sqrt{x-1}+\sqrt{x+3}+2\sqrt{\left(x-1\right)\left(x^2-3x+5\right)}=4-2x\)
b) \(\sqrt[4]{1-x}+\sqrt[4]{2-x}=\sqrt[4]{3-2x}\)
c) \(\sqrt{x+1}+\sqrt{x+10}=\sqrt{x+2}+\sqrt{x+5}\)
Giai phuong trinh
1/ \(\sqrt{x^2+4x+5}+\sqrt{x^2-6x+13}=3\)
2/ \(\sqrt{3x^2-18x+28}+\sqrt{4x^2-24x+45}=6x-x^2-5\)
3/ \(\sqrt{2x^2-4x+27}+\sqrt{3x^2-6x+12}=4x^2+8x+4\)
4/ \(\sqrt{x^2+x+7}+\sqrt{x^2+x+2}=\sqrt{3x^2+3x+19}\)
5/ \(\left(x+2\right)\left(x+3\right)-\sqrt{x^2+5x+1}=9\)
6/ \(\left(x+4\right)\left(x+1\right)-3\sqrt{x^2+5x+2}=6\)
7/ \(\sqrt{2x^2+3x+5}+\sqrt{2x^2-3x+5}=3\sqrt{x}\)
Giải phương trình bằng phương pháp bất đẳng thức
1, \(\sqrt{x^2-6x+11}+\sqrt{x^2-6x+13}+\sqrt[4]{x^2-4x+5}=3+\sqrt{2}\)
2, \(\sqrt{x-10}+\sqrt{30-x}=x^2-40x+400+2\sqrt{10}\)
3, \(x^2-3x+3,5=\sqrt{\left(x^2-2x+2\right)\left(x^2-4x+5\right)}\)
4, \(\sqrt{5x^3+3x^2+3x-2}=\dfrac{x^2}{2}+3x-\dfrac{1}{2}\)
5, \(2\sqrt{7x^3-11x^2+25x-12}=x^2+6x-1\)
Giải phương trình vô tỉ:
a) \(1+\frac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
b) \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-2\)
c) \(\sqrt{7x+7}+\sqrt{7x-6}+2\sqrt{49x^2+7x-42}=181-4x\)
d) \(\frac{\sqrt{x+4}+\sqrt{x-4}}{2}=x+\sqrt{x^2-16}-6\)
e) \(5\sqrt{x}+\frac{5}{2\sqrt{x}}=2x+\frac{1}{2x}+4\)
g) \(\sqrt{3x-2}+\sqrt{x-1}=4x-9+2\sqrt{3x^2-5x+2}\)
Giải phương trình sau
a,\(\sqrt{1+x}+\sqrt{8-x}+\sqrt{\left(x+1\right)\left(8-x\right)}=3\)
b, \(2\left(x^2+2\right)=5\sqrt{x^3+1}\)
c, \(x^2+x+3=3\sqrt{x^3+1}\)
d, \(2x^2+5x-1=7\sqrt{x^3-1}\)
e, \(\sqrt{2x+1}-\sqrt{3x}=x-1\)
f, \(\left(\sqrt{x+5}-\sqrt{x-2}\right)\left(1+\sqrt{x^2+7x+10}=3\right)\)
g, \(\sqrt{x^2-3x+2}-\sqrt{x+3}=\sqrt{x-2}-\sqrt{x^2+2x-3}\)
h, \(\sqrt{4x+1}-\sqrt{3x-2}=\frac{3+x}{5}\)
Giúp nhanh nha e cảm ơn
gpt : a) \(\frac{5x}{\sqrt{4-x^2}}+\frac{8}{x^2}+\frac{2x}{4-x^2}+\frac{5\sqrt{4-x^2}}{x}+4=0\)
b) \(\frac{2x}{\sqrt{8x^2+25}}+\frac{125}{x^2}-14=0\)
c) \(\left(x^3-3x+2\right)\sqrt{3x-2}-2x^3+6x^2-4x=0\)
d) \(\sqrt{x^2-x+6}+\frac{4}{x-1}=x^2+x\)
