Can anyone help with solve this extra credit math problem?
Tomcat6 asked:
I have an extra credit problem for math and I have tried to solve it and cannot get past this one step.
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I have an extra credit problem for math and I have tried to solve it and cannot get past this one step.
If the sum of two numbers is 1 and the sum of the cubes of the numbers is 3, what is the sum of the squares of the numbers? (fractional answer, no decimals)
So I made two equations.
a+b=1
a^3+b^3=3
I have tried substitution and everything and I cannot get it.
May 5th, 2010 at 7:01 am
Ugh, this can get ugly
This is an identity, verify yourself
a^3+b^3=(a+b)(a^2-ab+b^2)
substituting the values to reduce insanity
3=(1)(a^2-ab+b^2)
a^2+b^2=3+ab
Now we need ab.
(a+b)^3=a^3+3a^2b+3ab^2+b^3
(a+b)^3=a^3+b^3+3ab(a+b)
(1)^3=3+3ab(1)
1=3+3ab
ab=-2/3
a^2+b^2=3+(-2/3)
=3-2/3
=7/3
Or there abouts. You should check my math because I cannot decipher all these hat symbols. Who are I