SSC CGL 12 Aug 2017 Shift 1 Paper

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Question : 64 of 100

Marks: +1, -0

If

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

then what is the value of

(7 x+3 y-5 z) / {5x} \ ?

0
1
5
$33/5$

Solution:

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

On multiplying by ‘2’,

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

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

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

(x-y)^{2}+(y-z)^{2}+(z-x)^{2}=0

⇒

(x-y)^{2}=0, x=y

⇒

(y-z)^{2}=0, y=z

⇒

(z-x)^{2}=0, z=x

∴

{7 x+3 y-5 z}/{5 x}= {7 x+3 x-5 x}/{5 x}

= {10 x-5 x}/{5 x}= {5 x}/{5 x}=1

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