Question

giai pt

\(\sqrt{x^2+7}-\sqrt{x^2-5}=x-1\)

Answer 1

Ta có: \(\sqrt{x^2+7}-\sqrt{x^2-5}=x-1\) (ĐK: \(x\ge\sqrt{5}\) )

\(\Leftrightarrow\dfrac{x^2+7-16}{\sqrt{x^2+7}+4}-\dfrac{x^2-5-4}{\sqrt{x^2-5}+2}-\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(\dfrac{x+3}{\sqrt{x^2+7}+4}-\dfrac{x+3}{\sqrt{x^2-5}+2}-1\right)=0\)

Dễ thấy: \(\dfrac{x+3}{\sqrt{x^2+7}+4}-\dfrac{x+3}{\sqrt{x^2-5}+2}-1\ne0\)

\(\Leftrightarrow x=3\left(TM\right)\)

Answer 2

Nguyễn Thanh HằngXuân DinhBích Ngọc Huỳnh

Answer 3

Nguyễn Anh ThưHoàng Thị Anh Thưtrần thị diệu linh