Alg2.1.14

Find the value of x if $\sqrt{15-x\sqrt{14}}=\sqrt{8}-\sqrt{7}\,$

Squaring on both sides

$(\sqrt{15-x\sqrt{14}})^2=(\sqrt{8}-\sqrt{7})^2\,$

$15-x\sqrt{14}=8+7-2(\sqrt{8})(\sqrt{7})\,$

$15-x\sqrt{14}=15-2\sqrt{56}\,$

Simplifying

$x\sqrt{14}=2\sqrt{56}\,$

Squaring on bothsides we get

$(x\sqrt{14})^2=(2\sqrt{56})^2\,$

$14x^2=4(56)\,$

Hence $x^2=16\,$

$x=4\,$

The value of x is 4