Question

if abc=15,a+b+c=12,a^2+b^2+c^2=40 find a^3+b^3+c^3? Please answer fast tomorrow is my test!

Answer 1

Given abc = 15 ----- (1)

Given a + b + c = 12 ---- (2)

Given a^2 + b^2 + c^2 = 40 ---- (3)

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W.K.T a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca) --- (4)

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Now,

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

= > (12)^2 = 40 + 2(ab + bc + ca)

= > 144 = 40 + 2(ab + bc + ca)

= > 144 - 40 = 2(ab + bc + ca)

= > 104 = 2(ab + bc + ca)

= > ab + bc + ca = 52 ----- (5)

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Substitute (5) in (4), we get

= > a^3 + b^3 + c^3 - 3abc = (12)(40 - (ab + bc + ca))

= > a^3 + b^3 + c^3 - 3(15) = (12)(40 - 52)

= > a^3 + b^3 + c^3 - 45 = (12)(-12)

= > a^3 + b^3 + c^3 - 45 = -144

= > a^3 + b^3 + c^3 = -144 + 45

= > a^3 + b^3 + c^3 = -99

Hope this helps!