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

1.	If \(\sqrt{{15}-x\sqrt{14}}\) = √ 8 - √7 then x = ............A) 1 B) 0 C) 3 D) 4
Answer» 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) Correct option is D) 4

If \(\sqrt{{15}-x\sqrt{14}}\) = √ 8 - √7 then x = ............A) 1 B) 0 C) 3 D) 4

Answer»

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)

Correct option is D) 4