Question

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If a+b=3 and a^2+b^2=40 find the value of a^3+b^3

Answer 1

Hello Dear!!!

Here's your answer....

Given,

a+b = 3

a^2 + b^2 = 40

then,

a^3 + b^3 is

a^3 + b^3 = (a+b)(a^2 - ab + b^2)

(a+b) = 3

squaring on both sides...

(a+b)^2 = 3^2

a^2 + 2ab + b^2 = 9

40 + 2ab = 9

2ab = 9-40

2ab = -31

ab = -31/2

NOW,

a^3 + b^3 = (a+b)(a^2 - ab + b^2)
 
                = 3(40 -(-31/2))
 
                 = 3( 80+31/2)
 
                 = 3(111/2)
 
                  = 3(55.5)
 
                   = 166.5

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HOPE THIS HELPS YOU....