BPSC 65th Prelims Exam 15 Oct 2019 Solved Paper

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Question : 24 of 150

Marks: +1, -0

If

x^{3}-y^{3}=\;{117}/{8}

and

x-y=\;{3}/{2}

then the value of

x^{2}+x y+y^{2}

will be

1
$\;{5}/{8}$
$\;{39}/{4}$
$\;{39}/{8}$
None of the above/More than one of the above

Solution:

We know that

(x^{3}-y^{3})=(x-y)(x^{2}+x y+y^{2})

So, value of

x^{3}-y^{3}=\;{117}/{8}, x-y=\;{3}/{2}

Then,

\;{117}/{8}=(\;{3}/{2})(x^{2}+x y+y^{2})

So, By cross multiplication

(x^{2}+x y+y^{2})=\;{117}/{8} × \;{2}/{3}

=\;{39}/{4}

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