SSC CGL 8 Aug 2017 Shift 1 Paper

Question : 63 of 100

Marks: +1, -0

If a + b + c =27, then what is the value of

(a -7)^3 +(b -9 )^3 + (c -11 )^3

-3(a -7 )(b - 9)(c -11)?

Solution:

Let x = a - 7, y = b - 9, z = c - 11
Adding all three,
x + y + z = a + b + c - 27
∵ a + b + c = 27
⇒ x + y + z = 27 - 27
∴ x + y + z = 0

x ^3 + y ^3 + z^3 -3 x yz =0

⇒

(a -7)^3 + (b -9)^3 + (c -11 )^ 3

- 3 (a - 7 ) (b - 9 ) ( c - 11) = 0

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