Question

if √15-a√14 = √8+√7 find the value of a.

Answer 1

Answer:

$a =\sqrt{7} \frac{\sqrt{30} -4-\sqrt{14} }{14}$

Step-by-step explanation:

$\sqrt{15} - a\sqrt{14} = \sqrt{8} + \sqrt{7}$

$a\sqrt{14} = \sqrt{15} - \sqrt{8} - \sqrt{7}$

Dividing both sides by $\sqrt{14}$

$a = \frac{\sqrt{15} - \sqrt{8} - \sqrt{7}}{\sqrt{14} }$

$a = \frac{\sqrt{15*14}-\sqrt{8*14}-\sqrt{7*14} }{14}$

$a = \frac{\sqrt{210}-\sqrt{112}-\sqrt{98} }{14}$

$a = \frac{\sqrt{30}\sqrt{7} -4\sqrt{7}-7\sqrt{2} }{14}$

$a =\sqrt{7} \frac{\sqrt{30} -4-\sqrt{14} }{14}$//

HOPE IT HELPS.