SSC CGL Tier II 25 Oct 2015 Paper 1

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Question : 82 of 100

Marks: +1, -0

If

x^{2}+y^{2}+z^{2}=x y+y z+z x

then the value of

{3 x^{4}+7 y^{4}+5 z^{4}}/{5 x^{2} y^{2}+7 y^{2} z^{2}+3 z^{2} x^{2}}

is

2
1
0
–1

Solution:

(2)

x^{2}+y^{2}+z^{2}=x y+y z+z x

⇒ x^{2}+y^{2}+z^{2}-x y-y z-z x=0

⇒ 2 x^{2}+2 y^{2}+2 z^{2}-2 x y-2 y z- 2 z x=0

⇒x^{2}+y^{2}-2 x y+y^{2}+z^{2}-2 y z +x^{2}+z^{2}-2 z x=0

⇒(x-y)^{2}+(y-z)^{2}+(z-x)^{2}=0

∴ x-y=0⇒x=y

y-z=0 ⇒ y=z

z-x=0 ⇒ z=x

∴ x = y = z

[

If

a^{2}+b^{2}+c^{2}=0,

then

a=0, b=0, c=0 ]

∴ Expression

= {3 x^{4}+7 y^{4}+5 z^{4}}/{5 x^{2} y^{2}+7 y^{2} z^{2}+3 z^{2} x^{2}}

= {3 x^{4}+7 x^{4}+5 x^{4}}/{5 x^{4}+7 x^{4}+3 x^{4}}

= {15 x^{4}}/{15 x^{4}}=1

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