Question

Given:
\(a + b = 4\)
\(a^3 + b^3 = 28\)
What is \(a - b\)?

I got this:
\(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)
\(28 = 4(a^2 - ab + b^2)\)
How do I continue?

Answer 1

you can simplify it further

Answer 2

\(7 = a^2 - ab + b^2\)

Answer 3

I completed it by guess and check, but I need to do it algebraically

Answer 4

\[a^2 - ab + b^2 = (a+b)^2 - 3ab\]

Answer 5

@Waterineyes, (a - b)^2*

Answer 6

@waterineyes \[a^2 + b^2 -ab - ab = (a-b)^2 \ne (a+b)^2\]

Answer 7

\[\large{(a-b)^2=a^2+b^2-2ab}\]
\[\large{a^2+b^2+2ab=16}\]
\[\large{(a-b)^2=a^2+b^2+2ab-4ab=16-4ab}\]

Answer 8

\[(a + b)^2 - ab - ab =a^2 + b^2\]