Question

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

Answer 1

Answer:

$637$

Step-by-step 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.

$5 {}^{3} + {8}^{3}$

$125 + 512 = 637$