Question

If a + b = 6 and a2 + b2 = 20, find the value of a3+b3

Answer 1

Answer:

Given , a+b = 6 ( equation 1 )

a²+b² = 20 ( equation 2 )

Identify: (a +b)² = a² + b² + 2ab

Putting values of equation 1 and 2 here

( 6 )² = 20 + 2ab

36 - 20 = 2ab

16 = 2ab

8 = ab Or

ab = 8 ( equation 3 )

Now identity, a³+ b³ = (a+b)(a² + b² - ab)

Putting equation 1 , 2 and 3 here

a³ + b³ = (6) (20 - 8)

a³ + b³ = 6 × 12

a³+ b³ = 72

Step-by-step explanation:

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