Equations
a + b = 10 ... (1)
ab = 21 ...(2)
Answer: a³ + b³ = 370
• Form a new equation out of either eq. 1 or 2
b = 10 - a ... (3)
• Substitute b in second equation
-> a(10 - a) = 21
• Solve
-> 10a - a² = 21
-> 10a - a² - 21 = 0
• Simplify the quadratic expression
-> (a - 5)² - 4 = 0 (using completing the square method.
-> a - 5 = √4 or a - 5 = -√4
-> a - 5 = 2 or a - 5 = -2
-> a = 7 or a = 3
• Substitute values of a in second equation
When a = 7,
-> (7)b = 21
-> 7b = 21
-> b = 21/7
-> b = 3
When a = 3,
-> (3)b = 21
-> 3b = 21
-> b = 21/3
-> b = 7
(a, b) = (7, 3) or (3, 7)
• Substitute values for a and b into new equation
-> (7)³ + (3)³
-> 343 + 27
-> 370