Solve for b:
a + b = 3
(3 - b)^3 + b^3 = 18
Expand out terms of the left hand side:
9 b^2 - 27 b + 27 = 18
Divide both sides by 9:
b^2 - 3 b + 3 = 2
Subtract 3 from both sides:
b^2 - 3 b = -1
Add 9/4 to both sides:
b^2 - 3 b + 9/4 = 5/4
Write the left hand side as a square:
(b - 3/2)^2 = 5/4
Take the square root of both sides:
b - 3/2 = sqrt(5)/2 or b - 3/2 = -sqrt(5)/2
Add 3/2 to both sides:
b = 3/2 + sqrt(5)/2 or b - 3/2 = -sqrt(5)/2
Add 3/2 to both sides:
Answer: | b = 3/2 + sqrt(5)/2 and a = 1/2 (sqrt(5) - 3) or b = 3/2 - sqrt(5)/2 and a = 1/2 (-3 - sqrt(5))
+129840 a^3 + b^3 = 18
a + b = 3 → ( a + b) ^2 = 9 → a^2 + 2ab + b^2 = 9 → a ^2 + b^2 = 9 - 2ab
ab ????
a^3 + b^3 factors as
(a + b) ( a^2 - ab + b^2) ....so....
3 ( a^2 - ab + b^2) = 18 divide both sides by 3
( a^2 - ab + b^2) = 6
( [a^2 + b^2] - ab ) = 6
( [9 - 2ab] - ab) = 6
9 - 3ab = 6 subtract 9 from both sides
-3ab = -3 divide through by -3
ab = 1
