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SSC CGL 2020 PYQ — Question 62

SSC CGL Tier II - Quant - 18 Nov 2020 • Quantitative Aptitude • Q62

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If 8+2333+5=a3−b\frac{8 + 2\sqrt3}{3\sqrt3 + 5} ={a\sqrt3 - b}, then the value of a + b is equal to:

 

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 18

It is given that,

8+2333+5=a3−b\frac{8 + 2\sqrt3}{3\sqrt3 + 5} ={a\sqrt3 - b}

On solving the LHS part first we get,

8+2333+5×33−533−5\frac{8 + 2\sqrt3}{3\sqrt3 + 5} \times \frac{3\sqrt3 - 5}{3\sqrt3 - 5} = 243−40+18−1032\frac{24 \sqrt3 - 40 + 18 - 10\sqrt3}{2}

= 73−117\sqrt3 - 11

On comparing LHS and RHS we get,

a = 7 and b = 11

a + b = 7 + 11 = 18.