Lf a+b=10, ab=21 then a^3+b^3=

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

370

Step-by-step explanation:

a=3 or 7

b=7 or 3

3³+7³=370