\(2x^2-3x+10=3\sqrt{x^3+8}\)
\(\Leftrightarrow\left(x+2\right)+2\left(x^2-2x+4\right)=3\sqrt{x+2}.\sqrt{x^2-2x+4}\)
Đặt \(\left\{{}\begin{matrix}a=\sqrt{x+2}\\b=\sqrt{x^2-2x+4}\end{matrix}\right.\left(a,b\ge0\right)\)
Tìm x biết:
a.\(\sqrt{18x}+2\sqrt{8x}-3\sqrt{2x}=12\)
b.\(\sqrt{9x+18}+2\sqrt{36x+72}-\sqrt{4x+8}=26\)
c.\(\sqrt{\left(x-2\right)^2}=10\)
d.\(\sqrt{9x^2-6x+1}=15\)
e.\(\sqrt{3x+4}=3x-8\)
\(6x^2+2x+\sqrt[3]{3x^2+x+4}-10=0\)
\(x+1+\sqrt{x^24x+1}=3\sqrt{x}\)
\(x^2+2x\sqrt{x^2+4x+1}=3\sqrt{x}\)
\(\sqrt{x+8}+\dfrac{9x}{\sqrt{x+8}}-6\sqrt{x}=0\)
Giải phương trình \(3\sqrt{x^3+8}=2x^2-3x+10\)
a) \(\sqrt{x-3}-\sqrt{10-x}\)
b) \(\sqrt{x+4}+\dfrac{2-X}{x^2-16}\)
c) \(\dfrac{\sqrt{2x-3}}{\sqrt{x-4}}\)
d) \(\dfrac{\sqrt{2x-1}}{3x+2}\)
e) \(\dfrac{-2}{\sqrt{x^2+2x+2}}\)
Dùng biểu thức liên hợp:
a)\(\sqrt{2x-1}-\sqrt{x+1}=2x-4\). f)\(3\sqrt{x+1}+3\sqrt{x-1}=4x+1\).
b)\(\sqrt{2x^2-3x+10}+\sqrt{2x^2-5x+4}=x+3\).
c)\(\sqrt{x+2}-\sqrt{3-x}=x^2-6x+9\).
d)\(\sqrt{x}-\sqrt{x-1}=\sqrt{x+8}-\sqrt{x+3}.\)
e)\(\sqrt{x^2+x}-\sqrt{x^2-3}=\sqrt{2x^2-x-2}-\sqrt{2x^2+1}\)
a)\(\sqrt{x^2+2x+10}+x^2+2x+8=0\)
b)\(15x-2x^2-5=\sqrt{2x^2-15x+11}\)
c)\(\sqrt{9x^2+45}+\sqrt{16x^2+80}+3\sqrt{\frac{x^2+5}{16}}-\frac{1}{4}\sqrt{\frac{25x^2+15}{9}}=9\)
d)\(3x^2+21x+18+2\sqrt{x^2+7x+7}=2\)
e)\(\sqrt{x^2+3x+2}-2\sqrt{2x^2+6x+2}=-\sqrt{2}\)
f)\(\sqrt{x-1}+\sqrt{x+3}-\sqrt{x^2+2x-3}-1=0\)
Giải các phương tình sau:
a) \(x^3-3x^2+12x-5=2\sqrt{5x-1}+\sqrt[3]{3x-2}\)
b) \(4x^2+24x+17=2\sqrt{2x+5}+\sqrt[3]{4x+10}\)
c) \(2x^3-5x^2+16x-3=2\sqrt[3]{4x-1}+\sqrt[3]{2x+7}\)
d) \(2x^2+11x+12=2\sqrt{2x+3}+\sqrt[3]{x+2}\)
e) \(2x^2+3x-3-2\sqrt{2x+1}-\sqrt[3]{4x+2}=0\)
1. \(x^4-x^2+3x+5=2\sqrt{x+2}\)
2. \(\sqrt{x^2+x}+\sqrt{x-x^2}=2x+2\)
3. \(\left(\sqrt{x+5}-\sqrt{x+2}\right)\left(1+\sqrt{x^2+7x+10}\right)=3\)
4. \(\sqrt{2x^2-1}+\sqrt{x^2-3x+2}=\sqrt{2x^2+2x+3}+\sqrt{x^2-x+2}\)
bài 1
a) \(\sqrt{2X+1}\)
b)\(\sqrt{x^2-4}\)
c) \(\dfrac{3}{\sqrt{3X+5}}\)
d) \(\sqrt{X-3}-\sqrt{10-x}\)
e) \(\sqrt{x+4}+\dfrac{2-X}{x^2-16}\)
