Question

a+b=10 and ab=21 find a^3+b^3

Answer 1

a^3+b^3= (a+b)(a^2+b^2-ab)
a^3+b^3=10(58-21)
a^3+b^3=370
(a+b)^2-2ab =a^2+b^2
100- 42 =58= a^2+b^2

Answer 2

We know that a^3 + b^3 = (a + b)(a^2 + b^2 - ab)     ------------- (1)

Given, a+ b = 10, ab = 21

(a + b)^2 = a^2  + b^2 + 2ab

  100 = a^2 + b^2 + 2 * 21

 100 = a^2 + b^2 + 42

 a^2 + b^2 = 58       -------------------  (2)

Substitute equation (2) in (1)

a^3 + b^3 = 10 * 58 - 21
 
                 = 10 * 37

                = 370


Hope this helps!