SSC CGL 2 Sep 2016 Shif 2 Paper

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Question : 66 of 100

Marks: +1, -0

If k is the largest possible real number such that

p^4 + q^4

= (

p^2 + kpq + q^2

) (

p^2 – kpq + q^2

), then the value of k is

1
– $√2$
2
$√2$

Solution:

p^4 + q^4

=

(p^2)^2 + (q^2)^2

=

(p^2+q^2)^2 - 2p^2q^2

=

(p^2+q^2)^2

-

(√2pq)^2

=

(p^2+q^2 + √2pq)

(p^3=2+q^2 - √2 pq)

Clearly , k =

√2

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