Solve 3x+1-x-1=2?

# Solve $\sqrt{3x+1}-\sqrt{x-1}=2$?

1. A
$5$ and $1$
2. B
$-5$ and $1$
3. C
$5$ and $-1$
4. D
$-5$ and $-1$

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### Solution:

$⇒\sqrt{3x+1}-\sqrt{x-1}=2$
$⇒\sqrt{3x+1}=2+\sqrt{x-1}$
$⇒{\left(\sqrt{3x+1}\right)}^{2}={\left(2+\sqrt{x-1}\right)}^{2}$
$⇒3x+1=4+\left(x-1\right)+4\sqrt{x-1}$
$⇒\left(3x+1\right)-4-\left(x-1\right)=4\sqrt{x-1}$
$⇒2x-2=4\sqrt{x-1}$
$⇒2\left(x-1\right)=4\sqrt{x-1}$
$⇒\left(x-1\right)=2\sqrt{x-1}$
$⇒{\left(x-1\right)}^{2}={\left(2\sqrt{x-1}\right)}^{2}$
$⇒{x}^{2}-2x+1=4\left(x-1\right)$
$⇒{x}^{2}-6x+5=0$
$⇒\left(x-5\right)\left(x-1\right)=0$
or $x=1$

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