SSC CHSL 2021 PYQ — Question 61

The correct answer is Option 2 i.e. 90.

Given:

$(x+{{2} \over x})=7$

Formula Used:

(a + b)² = a² + 2ab + b² 

Explanation:

According to the given question,

$(x+{{2} \over x})=7$

Multiplying the equation by $\sqrt{2}$ on both sides, we get

⇒ $\sqrt{2}(x+{{2} \over x})=7\sqrt{2}$

⇒ $\sqrt{2}x+{{2}\sqrt{2} \over x}=7\sqrt{2}$

Now, squarying both sides, we get

 ⇒ $(\sqrt{2}x+{{2}\sqrt{2} \over x})^2 = (7\sqrt{2})^2$

⇒ $2x^2 +{8 \over x^2} + 2(\sqrt{2}x \times {2\sqrt{2} \over x}) = (7\sqrt{2})^2$

⇒ $2x^2 +{8 \over x^2} + 8 = 98$

⇒ $(2x^2+{{8} \over x^2}) = 90$

Hence the required answer is 90.