Question

If a and b are two positive real numbers such that a + b = 20 and ab = 4, then the value of a³ + b³ is:

• A. 7760
• B. 240
• C. 8000
• D. 8240

Answer 1

Answer:

A. 7760

Solution:

Given:

a and b are two positive real numbers such that a + b = 20 and ab = 4. We have to find the value of a³ + b³

Formula Used:

a3 + b³ = (a + b)³ – 3ab(a + b)

Calculation:

a³ + b³ = (a + b)³ – 3ab(a + b)

⇒ a³ + b³ = (20)³ – $3\times{4}\times{20}$       [∵ Given a + b = 20 and ab = 4]

⇒ a³ + b³ = 20 $\times$ (20² – 12)

⇒ a³ + b³ = 20 $\times$ (400 – 12)

⇒ a³ + b³ = 20 $\times$ 388

⇒ a³ + b³ = 7760

∴ Value of a³ + b³ is 7760