If ab=5 and a+b=1, then find the values of ab.
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If a + b = 5, then (a + b)^2 = a^2 + 2ab + b^2 = 25.
If a - b = 1, then (a - b)^2 = a^2 - 2ab + b^2 = 1.
Subtracting the bottom equation from the top equation yields 4ab = 24. That means that 8ab = 48.
Now we just need to know what a^2 + b^2 is. If 8ab = 48, then 2ab = 12.
We know that a^2 + 2ab + b^2 = 25. Substitute 2ab for 12:
a^2 + 12 + b^2 = 25
a^2 + b^2 = 13.
Therefore, 8ab(a^2 + b^2) = 48(13) = 624.
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