Question

If a+b=8 ab=15 then a³+b³=

Answer 1

Answer:

The value of a³ + b³ is 152.

Step-by-step-explanation:

We have given that,

a + b = 8

ab = 15

We have to find the value of a³ + b³.

We know that,

( a + b )³ = a³ + 3a²b + 3ab² + b³ - - [ Algebraic identity ]

⇒ ( a + b )³ - 3a²b - 3ab² = a³ + b³

⇒ a³ + b³ = ( a + b )³ - 3a²b - 3ab²

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

By substituting the given values in the above equation, we get,

a³ + b³ = ( a + b )³ - 3ab ( a + b )

⇒ a³ + b³ = ( 8 )³ - 3 × 15 ( 8 )

⇒ a³ + b³ = 512 - 45 × 8

⇒ a³ + b³ = 512 - 360

⇒ a³ + b³ = 152

∴ The value of a³ + b³ is 152.

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Additional Information:

Some Algebraic Identities:

1. ( a + b )² = a² + 2ab + b²

2. ( a - b )² = a² - 2ab + b²

3. a² - b² = ( a + b ) ( a - b )

4. ( a + b )³ = a³ + 3a²b + 3ab² + b³

5. ( a - b )³ = a³ - 3a²b + 3ab² - b³

6. a³ + b³ = ( a + b )³ - 3ab ( a + b )

7. a³ - b³ = ( a - b )³ + 3ab ( a - b )

8. ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ac