Question

Giải phương trình: \(\sqrt{x-1}+\sqrt{x+2}=\sqrt{x+34}-\sqrt{x+7}\)

Answer 1

\(\Leftrightarrow\sqrt{x-1}-1+\sqrt{x+2}-2=\sqrt{x+34}-6+3-\sqrt{x+7}\)

Answer 2

ĐK: x>=1

\(pt\Leftrightarrow\left(\sqrt{x-1}-1\right)+\left(\sqrt{x+2}-2\right)+\left(\sqrt{x+7}-3\right)-\left(\sqrt{x+34}-6\right)=0\)

\(\Leftrightarrow\frac{x-2}{\sqrt{x-1}+1}+\frac{x-2}{\sqrt{x+2}+2}+\frac{x-2}{\sqrt{x+7}+3}-\frac{x-2}{\sqrt{x+34}+6}=0\)

\(\Leftrightarrow\left(x-2\right)\left(\frac{1}{\sqrt{x-1}+1}+\frac{1}{\sqrt{x+2}+2}+\frac{1}{\sqrt{x+7}+3}-\frac{1}{\sqrt{x+34}+6}\right)=0\left(1\right)\)

Vì trong ngoặc lớn hơn 0 mọi x>=1

phương trình (1) <=> x-2=0 

<=>x=2 ( thỏa mãn)