CAT 2023 Surds and Indices Question (Medium)

Question

If , then is equal to

Accepted Answer

Given Equation 3 2 We are to find the value of --- Step 1 Let s simplify notation Let a quad quad b Given a b 3 2 Also a 2 5x 9 quad quad b 2 5x - 9 Subtract the two a 2 - b 2 5x 9 - 5x - 9 18 a - b a b 18 We already have , so a - b times 3 2 18 a - b 3 2 2 Rationalize the denominator a - b 2 2 - 4

CAT 2023

Quantitative

Surds and Indices

Medium

If $\sqrt{5 x+9}+\sqrt{5 x-9}=3(2+\sqrt{2})$ , then $\sqrt{10 x+9}$ is equal to

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