CAT 2025 Surds and Indices Question (Hard)

Question

If and , then the value of is

Accepted Answer

left x x right 2 x 2 x 2 2 25 2 27 Therefore, left x x right 3 Also, left x x right 3 x 3 x 3 3 left x x right Therefore, x 3 x 3 3 3 - 9 72 Also, left x 2 x 2 right 2 x 4 x 4 2 Therefore, x 4 x 4 25 2 - 2 623 Lastly, left x 4 x 4 right left x 3 x 3 right x 7 x 7 x x Therefore, x 7 x 7 623 72 - 3 44

CAT 2025

Quantitative

Surds and Indices

Hard

If $\left(x^2 + \dfrac{1}{x^2}\right) = 25$ and $x > 0$ , then the value of $\left(x^7 + \dfrac{1}{x^7}\right)$ is

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