Question

if a+b = 10 and a square +b square =58 find the value of a cube + b cube

Answer 1

a+b=10
a^2+b^2=58
a^3+b^3=??
(a+b)^2=a^2+b^2+2ab
(10)^2=58+2ab    (by putting the values)
100=58+2ab
100-58=2ab
42=2ab
42/2=2ab
21=2ab
now we will find a^3+b^3
a^3 + b^3 = (a + b)^3 − 3ab(a + b)
a^3 + b^3 = (10)^3-3*21(10)         (by putting the values) 
a^3 + b^3 = 1000-63*10
a^3 + b^3 = 1000-630
a^3 + b^3 = 370

Answer 2

Hello student,
Please find the answer to your question below
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