SOLUTION: Simplify the expressions. a+b=3 and a^2+b^2=30, find a^3+b^3 Please help i really need an answer. Thanks!

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Question 897680: Simplify the expressions.
a+b=3 and a^2+b^2=30, find a^3+b^3

Please help i really need an answer. Thanks!
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
a+b=3 and a^2+b^2=30
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b = 3-a
a^2 + (3-a)^2 = 30
2a^2 - 6a + 9 = 30
2a^2 - 6a - 27 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=252 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5.46862696659689, -2.46862696659689. Here's your graph:

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Someone has to cube those and add them.
You need the practice more than I do.
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= (27/8)*44
= 297/2