Question

if a + b+ c =12,a^2+b^2+c^2=90 ,find values of a^3 +b^3+c^3_3ab

Answer 1

Heya !!

Here's your answer !!!

a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ac)

Given, a+b+c = 12, a²+b²+c² = 90

(a+b+c)² = (a²+b²+c²)+2(ab+bc+ac)

12² = 90+2×(ab+bc+ac)

54 = 2(ab+bc+ac)

(ab+bc+ac) = 54/2 = 27

a³+b³+c³-3abc = 12×90-(27)
= 12× 63
= 756

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