Question

if a+b= 10 , a²+b²=58 find a³+b³

Answer 1

we can easly find that a=3 and b=7 so a³ +b³ =370

Answer 2

Answer:

We know that

(a + b)² = a² + b² + 2ab

Putting a + b = 10 and a² + b² = 58, we get

10² = 58 + 2ab

=> 100 = 58 + 2ab

=> 100 - 58 = 2ab

=> 42 = 2ab

=> ab = 21

THUS, WE HAVE

a + b = 10 and ab = 21

Now,

(a + b)³ = a³ + b³ + 3ab (a+b)

=> 10³ = a³ + b³ + 3 × 21 × 10

=> 1000 = a³ + b³ + 630

=> 1000 - 630 = a³ + b³

=> 370 = a³ + b³

=> a³ + b³ = 370.

Hence , the value of a³ + b³ is 370.