Question

Evaluate x³ - y ³, if x+ y = 7 and x y = 12​

Answer 1

Answer:

Let’s focus on equation 1. We want to isolate x. Subtract y from both sides;

x = 7 - y

Substitute x = 7 - y into equation 2: xy=12;

(7 - y)y = 12

Distribute;

7y - y^2 = 12

Subtract 12 from both sides;

7y - y^2 - 12

Order by terms;

-y^2 + 7y - 12

Quadratic Equation Formula; (-b +-√(b^2–4ac)) / (2a)

a = -1, b = 7, c = -12

Skipping the explanation of the formula because it is messy

y = 3

y = 4

Plug each solution into the original equation 1;

x + y = 7

Substitute y for 3 and y for 4;

x + 3 = 7

x + 4 = 7

Eq. 1; Subtract 3 from both sides

x = 4

Eq. 2; Subtract 4 from both sides

x = 3

Solutions: (3, 4) (4, 3)

Eq. 1: Substitute x for 3 and y for 4

3^3 + 4^3

Simplify

27 + 64

Combine like terms

91

Eq. 2: Substitute x for 4 and y for 3

4^3 + 3^3

Simplify

64 + 27

Combine like terms

91

Answer: 91

Answer 2

Answer:

I hope it's helpful you☺