algebra
posted by janice .
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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