Question

If 8ab(a^2+b^2)=24 then what is the value of a+b and a-b?

Answer 1

Step-by-step explanation:

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)