Question

a+b=10
a²+b²=58
Find a³+b³

Answer 1

$<b>Solution:$

a³ + b³ = (a + b) (a² - ab + b²)

= 10 (58 - ab)

But (a + b)² = a² + 2ab + b² = 58 + 2ab

also (a+b)²= 10² = 100 since a+b=10

58+2ab=100

=> 2ab =100-58=42

=> ab = 21

=>a³ + b³ = (a + b) (a² - ab + b²)

= 10 (58 - ab)

=10 × (58 - 21)

= 370

Hope it helps!

Answer 2

here is your answer OK

( a + b)2 = a2 + b2 + 2ab

100 = 58 + 2ab

42 = 2ab

ab = 21

(a + b)3 = a3 + b3 + 3ab(a + b)

1000 = a3 +b3 + 3*21(10)

1000 = a3 +b3 + 630

a3 +b3 = 370