I came across an interesting system of equations the other day:

a + b = 14

a^3 + b^3 = 812

For some reason, I can't solve it. Help!

Guest Oct 26, 2020

#1**0 **

a + b = 14, a^3 + b^3 = 812, solve for a, b

Use substitution to get:

a=14 - b

(14 - b)^3 + b^3 =812

Solve for b:

(14 - b)^3 + b^3 = 812

Expand out terms of the left hand side:

42 b^2 - 588 b + 2744 = 812

Divide both sides by 42:

b^2 - 14 b + 196/3 = 58/3

Subtract 196/3 from both sides:

b^2 - 14 b = -46

Add 49 to both sides:

b^2 - 14 b + 49 = 3

Write the left hand side as a square:

(b - 7)^2 = 3

Take the square root of both sides:

b - 7 = sqrt(3) or b - 7 = -sqrt(3)

Add 7 to both sides:

b = 7 + sqrt(3) or b - 7 = -sqrt(3)

Add 7 to both sides:

b = 7 + sqrt(3) or b = 7 - sqrt(3)

Sub this value of b into: a + b = 14 and should get:

**a = 7 - sqrt(3) and b = 7 + sqrt(3) a = 7 + sqrt(3) and b = 7 - sqrt(3)**

Guest Oct 26, 2020