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How do you solve $\sqrt{x + 3} - \sqrt{x - 1} = 1$ $sqrt(x+3)-sqrt(x-1)=1$ ?

1 Answer

Aug 31, 2016

$x = \frac{13}{4} = 3 \frac{1}{4}$ $color(green)(x=13/4 = 3 1/4)$

Explanation:

Given
$XXX \sqrt{x + 3} - \sqrt{x - 1} = 1$ $color(white)("XXX")sqrt(x+3)-sqrt(x-1)=1$

$XXX \to \sqrt{x + 3} = 1 + \sqrt{x - 1}$ $color(white)("XXX")rarr sqrt(x+3)=1+sqrt(x-1)$

Squaring both sides:
$color(white)("XXX")cancel(x)+3=cancel(1)+2sqrt(x-1)+cancel(x)cancel(-1)$

$color(white)("XXX")rarr 2sqrt(x-1)=3$

$color(white)("XXX")rarr sqrt(x-1)=3/2$

Squaring both sides again
$color(white)("XXX")rarr x-1=9/4$

$color(white)("XXX")rarr x=13/4$

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