Question

If a + b = 10 and ab = 24, then what is the value of a3 – b3

Answer 1

Question:-

If a + b = 10 and ab = 24, then what is the value of a³ - b³

$\huge\bf\underline\purple{Solution}$

${a}^{3} - {b}^{3} = {(a + b)}^{3} - 3ab(a + b)$

Putting the values of (a + b) = 10 and ab = 24

=> a³ - b³ = (10)³ - 3 × 24 (10)

=> a³ - b³ = 1000 - 72 × 10

=> a³ - b³ = 1000 - 720

=> a³ - b³ = 280

Hence, the value of a³ - b³ is 280 respectively.

Indentity used :-

${a}^{3} - {b}^{3} = {(a + b)}^{3} - 3ab(a + b)$

Some important identities :-

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• a² + b² = (a + b)² - 2ab
• a² - b² = (a + b)(a - b)