\(S=-\frac{1}{2}\left(3x+3-2\sqrt{2x^2+5x+2}+x+7-4\sqrt{x+3}\right)+5\)
\(=-\frac{1}{2}\left[\frac{\left(x-1\right)^2}{3x+3+2\sqrt{2x^2+5x+2}}+\frac{\left(x-1\right)^2}{x+7+4\sqrt{x+3}}\right]+5\le5\)
\(S_{max}=5\) khi \(x=1\)
Violympic toán 9
Các câu hỏi tương tự
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+2sqrt{2x^2+5x+3}-2
c) sqrt{7x+7}+sqrt{7x-6}+2sqrt{49x^2+7x-42}181-4x
d) frac{sqrt{x+4}+sqrt{x-4}}{2}x+sqrt{x^2-16}-6
e) 5sqrt{x}+frac{5}{2sqrt{x}}2x+frac{1}{2x}+4
g) sqrt{3x-2}+sqrt{x-1}4x-9+2sqrt{3x^2-5x+2}
Đọc tiếp
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) \(\sqrt{3x-2}+\sqrt{x-1}=4x-9+2\sqrt{3x^2-5x+2}\)
Cho A=\(\left(\frac{2}{\sqrt{x}-2}+\frac{3}{2\sqrt{x}+1}-\frac{5\sqrt{x}-7}{2x-3\sqrt{x}-2}\right):\frac{2\sqrt{x}+3}{5x-10\sqrt{x}}\)
tìm x để A nguyên
Giair phương trình
a, \(3\sqrt{\left(x+1\right)\left(x-3\right)}+x^2-2x=7\)
b, \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-16\)
c, \(\left(x^2-4\right)+4\left(x-2\right).\sqrt{\frac{x+2}{x-2}}=3\)
d, \(\frac{9}{x^2}+\frac{2x}{\sqrt{2x^2+9}}=1\)
e, \(3\sqrt{2+x}-6\sqrt{2-x}+4\sqrt{4-x^2}=10-3x\)
Cho x,y,z>0 thỏa mãn \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=3\). Tìm Max \(P=\frac{1}{\sqrt{2x^2+y^2+3}}+\frac{1}{\sqrt{2y^2+z^2+3}}+\frac{1}{\sqrt{2z^2+x^2+3}}\)
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
Đọc tiếp
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^2right)x^3-3x^2+2x+6
b)x^2+x+12sqrt{x+1}36
c)3x-1+frac{x-1}{4x}sqrt{3x+1}
d)sqrt{x^2+12}-3xsqrt{x^2+5}-5
e)4x^2+12+sqrt{x-1}4left(xsqrt{5x-1}+sqrt{9-5x}right)
f)4x^3-25x^2+43x+xsqrt{3x-2}22+sqrt{3x-2}
g)2left(x+1right)sqrt{x}+sqrt{3left(2x^3+5x^2+4x+1right)}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-2right|
k)sqrt{2x^3+3x^2-1}2x^2+2x-x^3-1
l)sqrt{x^2+x-2}+x^2sqrt{2left(x-1right)}+1
Đọc tiếp
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)\(\sqrt{x^2+x-2}+x^2=\sqrt{2\left(x-1\right)}+1\)
1 tháng 1 2020 lúc 22:36
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) \(\sqrt{x^2-x+6}+\frac{4}{x-1}=x^2+x\)
(Gấp xin hãy giải hộ vs ạ chiều e học rùi . E xin cảm ơn) GIẢI PHƯƠNG TRÌNH SAU
1)frac{3}{sqrt{x-2}+3}-frac{1}{sqrt{x+6}+3}2
2)sqrt{x^2+2x}+sqrt{2x-1}sqrt{3x^2+4x+1}
4) ( 3x+1).sqrt{2x^2-1}5x2+frac{3x}{2}
5) x2+7x(2x+1).sqrt{x^2+x+6}
6) sqrt{5x^2+6x+5}. (5x2+6x++6)4x. (16x2+1)
Đọc tiếp
(Gấp xin hãy giải hộ vs ạ chiều e học rùi . E xin cảm ơn) GIẢI PHƯƠNG TRÌNH SAU
1)\(\frac{3}{\sqrt{x-2}+3}\)-\(\frac{1}{\sqrt{x+6}+3}\)=2
2)\(\sqrt{x^2+2x}\)+\(\sqrt{2x-1}\)=\(\sqrt{3x^2+4x+1}\)
4) ( 3x+1).\(\sqrt{2x^2-1}\)=5x2+\(\frac{3x}{2}\)
5) x2+7x=(2x+1).\(\sqrt{x^2+x+6}\)
6) \(\sqrt{5x^2+6x+5}\). (5x2+6x++6)=4x. (16x2+1)
Giải phương trình:
1, \(4\left(2x^2+1\right)+3\left(x^2-2x\right)\sqrt{2x-1}=2\left(x^3+5x\right)\)
2, \(\sqrt{5x^2+4x}-\sqrt{x^2-3x-18}=5\sqrt{x}\)
3, \(\sqrt{5x^2-14x+9}-\sqrt{x^2-x-20}=5\sqrt{x+1}\)