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If a + b = 7 and a^3 + b^3 = 42, what is the value of the sum a^2 + b^2?  Express your answer as a common fraction.

 Jun 17, 2021
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a^3 + b^3 = 42

(a+b)(a^2 - ab + b^2) = 42

a^2 - ab + b^2 = 6

(a+b)^2 - 3ab = 6

49 - 3ab = 6

ab = 43/3

 

a^2 - ab + b^2 = 6

a^2 - 43/3 + b^2 = 6

a^2 + b^2 = 20 1/3

 

=^._.^=

 Jun 17, 2021

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