Question

If a+b=13, and ab-40, then find a3+b3​

Answer 1

`637`

Explanation:

Step 1: Set Up System of Equations

`a + b = 13`

`ab = 40`

Solve for a in the first equation

`a = 13 - b`

Subsitur that in for the 2nd equation

`(1 3 - b)(b) = 40`

`- b {}^(2) + 13b = 40`

`- {b}^(2) + 13b - 40`

`- (b - 5)(b - 8)`

Set each monomial to zero

Think of a number that adds to 13 and multiply to 40.

Th

`b = 5`

`b = 8`

So the answer is 5 and 8. Remember factos are interchangeable so a and b can be either 8 or 5.

Cubed both 5 and 8.

`5 {}^(3) + {8}^(3)`

`125 + 512 = 637`