# algebra

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if a+b=1 and a squared + b squared=2
what does a to the 3rd + b to the 3rd equal?

If b is 1, b cubed is one.

That would work for the first half, but doesn't extend to a to the 3rd+b to the 3rd and what weould 2 squard be? Thank you so much for helping

Are you saying:

if a+b=1 and if a^2 + b^2 =2 find a^3 + b^3 ??

if so, then you have to play with the expansion of (a+b)^??

(a+b)^2 = a^2 + 2ab + b^2 subbing in your given
1 = 2 + 2ab ------> ab = -1/2

then (a+b)^3 = a^3 + 3(a^2)b + 3a(b^2) + b^3
(a+b)^3 = a^3 + b^3 + 3ab(a + b)
1 = a^3 + b^3 + 3(-1/2)(1)

a^3 + b^3 = -3/2 - 1
= -5/2

oops on the last two lines
should have been

a^3 + b^3 = 3/2 + 1
= 5/2

THANK YOU!!

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