​ If √{15 - x√{14}} = √ 8 - √7 then x = ............ ​

Question

If \(\sqrt{{15}-x\sqrt{14}}\) = √ 8 - √7 then x = ............

A) 1 

B) 0 

C) 3 

D) 4

Answer 1

Correct option is (D) 4

Given that \(\sqrt{15-x\sqrt{14}}=\sqrt8-\sqrt7\)

\(\Rightarrow\) \(15-x\sqrt{14}=(\sqrt8-\sqrt7)^2\)    (By squaring both sides)

\(\Rightarrow\) \(15-x\sqrt{14}=8+7-2\sqrt8\times\sqrt7\)   \((\because(a-b)^2=a^2+b^2-2ab\) Here \(a=\sqrt8\,\&\,b=\sqrt{7})\)

\(\Rightarrow\) \(15-x\sqrt{14}=15-4\sqrt{14}\)

\(\therefore\) x = 4   (By comparing)

Answer 2

Correct option is D) 4