SSC CGL 16 Aug 2015 Shift 2 Paper

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Question : 137 of 200

Marks: +1, -0

If a + b – c = 14 then the value of

2b^2c^2 + 2c^2a^2

+

2a^2b^2 –a^4 – b^4 – c^4

7
0
14
28
None of the above

Solution:

Expression =

2b^2c^2 + 2c^2a^2

+

2a^2b^2 – a^4 – b^4 – c^4

=

4b^2c^2

– (

2b^2c^2 – 2c^2a^2 – 2a^2b^2 + a^4 + b^4 + c^4

)
=

(2bc)^2

–

(a^2 – b^2 – c^2)^2

= (2bc +

a^2 – b^2 – c^2

) (2bc –

a^2 + b^2 + c^2

)
=

(a^2 – (b^2 + c^2 – 2bc))

(b^2 + c^2 + 2bc – a^2)

=

(a^2 – (b – c)^2)

((b + c)^2 – a^2)

= (a – b + c) (a + b – c)
(a + b + c) (b + c – a)
If a + b – c = 0,
∴ Expression = 0.

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