AP ICET 2016 Paper

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Question : 102 of 200

Marks: +1, -0

If

a:b=2:5

,then

a^{2}-ab+b^{2}:a^{2}+ab+b^{2}=

$19:39$
$6:13$
$17:39$
$13:39$

Solution:

Given

a:b=2:5

{a^{2}-ab+b^{2}}/{a^{2}+ab+b^{2}}={({a}/{b})^{2}-({a}/{b})+1}/{({a}/{b})^{2}+({a}/{b})+1}={({2}/{5})^{2}-{2}/{5}+1}/{({2}/{5})^{2}+{2}/{5}+1}

={4-10+25}/{4+10+25}=19/39

Aliter Let

a=2k,b=5k

⇒{a^{2}-ab+b^{2}}/{a^{2}+ab+b^{2}}={(2^{2}-2×5+5^{2})k^{2}}/{(2^{2}+2×5+5^{2})k^{2}}={19}/{39}

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