Question

giải phương trình: \(\dfrac{\sqrt{5x+7}}{\sqrt{x+3}}=4\)

Answer 1

\(\dfrac{\sqrt{5x+7}}{\sqrt{x+3}}=4\left(x\ge-\dfrac{7}{5};x\ne-3\right)\)

\(< =>\sqrt{5x+7}=4\sqrt{x+3}\)

\(< =>5x+7=16\left(x+3\right)\)

`<=>5x+7=16x+48`

`<=>5x-16x=48-7`

`<=>-11x=41`

`<=>x=-41/11(ktm)`

Vậy pt vô nghiệm

Answer 2

\(\dfrac{\sqrt{5x+7}}{\sqrt{x+3}}=4\) ĐK: \(x\ge-\dfrac{7}{5}\)

\(\Rightarrow\sqrt{5x+7}=4\sqrt{x+3}\)

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

\(\Leftrightarrow5x+7=16\left(x+3\right)\)

\(\Leftrightarrow5x+7=16x+48\)

\(\Leftrightarrow16x-5x=7-48\)

\(\Leftrightarrow11x=-41\)

\(\Leftrightarrow x=-\dfrac{41}{11}\) (loại)

Vậy \(S=\varnothing\).