Question

If a-b=7 and a^3-b^3=133 then find ab and a^2+b^2

Answer 1

a+b =7

a^3 +b^3 =133

a^2 +b^2 =?

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

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

7^3=133+3ab(7)

343-133=3ab(7)

210=3ab(7)

3ab=30

ab=10

therefore,

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

49=a^2+b^2+20

a^2+b^2=29

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