Question

If a + b = 10 and $\frac{3}{7}$ of ab = 9, then the value of a³ + b³ is:

• A. 350
• B. 370
• C. 270
• D. 360

Answer 1

Answer:

B. 370

Solution:

Given:

a + b = 10 

$\frac{3}{7}$ of ab = 9

Formula:

a³ + b³ = (a + b) [(a + b)² - 3ab]

Calculation:

$\frac{3}{7}$ of ab = 9

⇒ ab = $9\times(\frac{7}{3})$

⇒ ab = 21

a³ + b³ = (a + b) [(a + b)² - 3ab]

⇒ a³ + b³ = 10 $\times$ [10² - 3 $\times$ 21]

⇒ a³ + b³ = 10 $\times$ [100 - 63]

⇒ a³ + b³ = 10 $\times$ 37 = 370.