Question

[Ngọc Quách]

Giải phương trình:

a) \(4\left(x+1\right)^2\)=\(\left(2x+10\right)\left(1-\sqrt{3-2x}\right)\)

b) \(\frac{1}{x+\sqrt{x^2+x}}+\frac{1}{x-\sqrt{x^2+x}}=x\)

c) \(\sqrt{2x+4}-2\sqrt{2-x}=\frac{12x-8}{\sqrt{9x^2+16}}\)

Answer 1

[Thắng Nguyễn]

xem lại đề câu 1đi nhé 

Answer 2

[Thắng Nguyễn]

b)\(\frac{1}{x+\sqrt{x^2+x}}+\frac{1}{x-\sqrt{x^2+x}}=x\)

\(\Leftrightarrow\frac{x-\sqrt{x^2+x}}{\left(x+\sqrt{x^2+x}\right)\left(x-\sqrt{x^2+x}\right)}+\frac{x+\sqrt{x^2+x}}{\left(x-\sqrt{x^2+x}\right)\left(x+\sqrt{x^2+x}\right)}-\frac{x\left(x+\sqrt{x^2+x}\right)\left(x-\sqrt{x^2+x}\right)}{\left(x+\sqrt{x^2+x}\right)\left(x-\sqrt{x^2+x}\right)}=0\)

\(\Leftrightarrow\frac{x-\sqrt{x^2+x}+x+\sqrt{x^2+x}-x^2}{\left(x+\sqrt{x^2+x}\right)\left(x-\sqrt{x^2+x}\right)}=0\)

\(\Leftrightarrow\frac{-x^2+2x}{\left(x+\sqrt{x^2+x}\right)\left(x-\sqrt{x^2+x}\right)}=0\)

\(\Leftrightarrow\frac{-x\left(x+2\right)}{\left(x+\sqrt{x^2+x}\right)\left(x-\sqrt{x^2+x}\right)}=0\)

Dễ thấy: x=0 ko là nghiệm nên \(x+2=0\Rightarrow x=-2\)

c)\(\sqrt{2x+4}-2\sqrt{2-x}=\frac{12x-8}{\sqrt{9x^2+16}}\)

\(\Leftrightarrow\frac{\left(2x+4\right)-4\left(2-x\right)}{\sqrt{2x+4}+2\sqrt{2-x}}=\frac{4\left(3x-2\right)}{\sqrt{9x^2+16}}\)

\(\Leftrightarrow\frac{2\left(3x-2\right)}{\sqrt{2x+4}+2\sqrt{2-x}}=\frac{4\left(3x-2\right)}{\sqrt{9x^2+16}}\)

\(\Leftrightarrow\frac{2\left(3x-2\right)}{\sqrt{2x+4}+2\sqrt{2-x}}-\frac{4\left(3x-2\right)}{\sqrt{9x^2+16}}=0\)

\(\Leftrightarrow\left(3x-2\right)\left(\frac{2}{\sqrt{2x+4}+2\sqrt{2-x}}-\frac{4}{\sqrt{9x^2+16}}\right)=0\)

\(\Leftrightarrow x=\frac{2}{3}\)