Question

Gpt:

a. \(5x+2\sqrt{x+1}-\sqrt{1-x}=-3\)

Answer 1

\(5x+2\sqrt{x+1}-\sqrt{1-x}=-3\) \(\left(-1\le x\le1\right)\)

\(\Leftrightarrow\left(5x+3\right)+\dfrac{4\left(x+1\right)-\left(1-x\right)}{2\sqrt{x+1}+\sqrt{1-x}}=0\)

\(\Leftrightarrow\left(5x+3\right)+\dfrac{5x+3}{2\sqrt{x+1}+\sqrt{1-x}}=0\)

\(\Leftrightarrow\left(5x+3\right)\left(1+\dfrac{1}{2\sqrt{x+1}+\sqrt{1-x}}\right)=0\)

Pt \(1+\dfrac{1}{2\sqrt{x+1}+\sqrt{1-x}}=0\left(VT>0\right)\)

=> 5x + 3 = 0

<=> x = - 0,6 (nhận)