SSC CHSL 15 Oct 2020 Shift 3 Paper

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Question : 75 of 100

Marks: +1, -0

If

a=355, b=356, c=357

, then find the value of

a^{3}+b^{3}+c^{3}-3 a b c

.

3208
3202
3206
3204

Solution:

Given,

a=355, b=356, c=357

We know that,

a^{3}+b^{3}+c^{3}-3 a b c

=(a+b+c)

(a^{2}+b^{2}+c^{2}-a b-b c-c a)

={1}/{2} ×(a+b+c) (2 a^{2}+2 b^{2}+2 c^{2}-2 a b-2 b c-2 c a)

={(a+b+c)}/{2} ×[(a-b)^{2} +(b-c)^{2}+(c-a)^{2}]

={(355+356+357)}/{2} ×[(355-356)^{2}+(356-357)^{2}+(357-355)^{2}]

={1068}/{2} ×[1+1+4]

= 3204

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