First slide

Theory of expressions

Question

If $α$ and $β$ be two roots of the equation $x^{2} - 64 x$ +256=0. Then, value of ${(\frac{α^{3}}{β^{5}})}^{1 / 8} + {(\frac{β^{3}}{α^{5}})}^{1 / 8} is$

Moderate

A

2
B

3
C

1
D

4

Solution

Given quadratic equation $x^{2} - 64 x + 256 = 0$ having roots $α$ and $β$ , so
$α + β = 64 and αβ = 256$
Now, ${(\frac{α^{3}}{β^{5}})}^{1 / 8} + {(\frac{β^{3}}{α^{5}})}^{1 / 8} = \frac{α + β}{(αβ)^{5 / 8}}$
$= \frac{64}{(256)^{5 / 8}} = \frac{64}{2^{5}} = \frac{64}{32} = 2$

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