AP ICET 2019 Shift 1 Paper

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Question : 123 of 200

Marks: +1, -0

If α and β are the roots of the equation

8x^2-3x-27

= 0. then the value of

(α^2/β)^{1/3}+(β^2/α)^{1/3}

=

$1/4$
$1/3$
$3/2$
$1/9$
None of the above

Solution:

8x^2 – 3x – 27 = 0

Given α,β are the roots of it, then

α+β=3/8,αβ={-27}/8

({α^{2}}/{β})^{{1}/{3}}+({β^{2}}/{α})^{{1}/{3}}={(α^{3})^{{1}/{3}}+(β^{3})^{{1}/{3}}}/{(α β)^{{1}/{3}}}={α+β}/{(α β)^{{1}/{3}}}

={{3}/{8}}/{({-27}/{8})^{{1}/{3}}}={3}/{8} ×{-2}/{3}={-1}/{4}

Ans:

({-1}/{4})

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