AP ICET 2015 Paper

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Question : 77 of 200

Marks: +1, -0

If a, b, c are real and

a+b+c=0

, then

x^{a^{2}b^{-1}c^{-1}}x^{a^{-1}b^{2}c^{-1}}x^{a^{-1}b^{-1}c^{2}}

1
$x^2$
$x^3$
$x^{-2}$

Solution:

Given :

a+b+c=0

, a, b, c, are real numbers

x^{a^{2}b^{-1}c^{-1}}x^{a^{-1}b^{2}c^{-1}}x^{a^{-1}b^{-1}c^{2}}

x^({a^{2}}/{bc}+{b^{2}}/{ac}+{c^{2}}/{ab})=x^({a^{3}+b^{3}+c^{3}}/{abc})={3abc}/{x^{abc}}

=x^3

[

a^3+b^3+c^3=3abc

when a + b + c = 0]

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