Question

If a+b+c=15 and a2+b2+c2=83,find the value of a3+b3+c3-3abc

Answer 1

a3+b3+c3-3abc

=( a+b+c) (a2+b2+c2-ab-bc-ca)

using this rule you can find out the value.

Answer 2

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

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

15^2 = 83 + 2(ab + bc + ab)

(15^2 – 83) / 2 = ab + bc + ab

(a + b + c)^3 = a^3 + b^3 + c^3 - 3abc + 3 (a^2×b + a×b^2 + a^2×c + a×c^2 + b^2×c + b×c^2 + 3abc)

(a + b + c)^3 = Y + 3 (a + b + c)(ab + bc + ac)

15^3 = Y + 3(15)[(15^2 – 83) /2]

Y = 15^3 - 3(15)[(15^2 - 83) /2]

Y = 15^3 - 45×71

Y = 45 (75–71)

Y = 45×4

Y = 180

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