Question

a+b=10 and ab is =20 then the value of a cube +b cube

Answer 1

Answer :-

400

Solution :-

We know that

(a + b)³ = a³ + b³ + 3ab(a + b)

Here

• a + b = 10

• ab = 20

By substituting the values

⇒ (10)³ = a³ + b³ + 3(20)(10)

⇒ 1000 = a³ + b³ + 60(10)

⇒ 1000 = a³ + b³ + 600

Transpose 600 to RHS ( + 600 becomes - 600)

⇒ 1000 - 600 = a³ + b³

⇒ 400 = a³ + b³

⇒ a³ + b³ = 400

Therefore the value of a³ + b³ is 400.

Verification :-

(a + b)³ = a³ + b³ + 3ab(a + b)

⇒ (10)³ = 400 + 3(20)(10)

⇒ 1000 = 400 + 60(10)

⇒ 1000 = 400 + 600

⇒ 1000 = 1000

Identity used :-

• (a + b)³ = a³ + b³ + 3ab(a + b)