SSC CGL 11 Aug 2017 Shift 1 Paper

Question : 62 of 100

Marks: +1, -0

If a + b + c = 9 and ab + bc + ca = 18, then what is the value of

a^3 + b^3 + c^3 - 3 abc

Solution:

a+b+c=9

ab + bc + ca = 18

(a + b + c)^2 = (9)^2

⇒

a^2 + b^2 + c^2 + 2 (ab + bc + ca)= 81

⇒

a^2 + b^2 + c^2 + 2 × 1 8 = 81

⇒

a^2 + b^2 + c^2 = 8 1 - 3 6 = 4 5

∴

a^3 + b^3 + c^3 -3abc = ( a + b + c)

(a^2 + b^2 + c^2 - a b - bc - ca)

= 9(45-18) = 9× 27=243

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