Question

Giải phương trình \(\sqrt{x+7}-\sqrt{x-82}=x-2017\)

Answer 1

\(\sqrt{x+7}-45-\sqrt{x-82}+44=x-2018\)

\(\dfrac{\left(\sqrt{x+7}-45\right)\left(\sqrt{x+7}+45\right)}{\sqrt{x+7}+45}-\dfrac{\left(\sqrt{x-82}-44\right)\left(\sqrt{x-82}+44\right)}{\sqrt{x-82}+44}-\left(x-2018\right)=0\)

\(\dfrac{x-2018}{\sqrt{x+7}+45}-\dfrac{x-2018}{\sqrt{x-82}+44}-\left(x-2018\right)=0\) \(\left(x-2018\right)\left(\dfrac{1}{\sqrt{x+7}+45}-\dfrac{1}{\sqrt{x-82}+44}-1\right)=0\)

mà \(\dfrac{1}{\sqrt{x+7}+45}-\dfrac{1}{\sqrt{x-82}+44}-1< 0\)

\(\Rightarrow x=2018\)