If a − b = 4 and ab = 21, find the value of a^3 − b^3. - www.mathselab.com

If a − b = 4 and ab = 21, find the value of a^3 − b^3.

Question


If a − b = 4 and ab = 21, find the value of a3 − b3.


A. 312
B. 306
C. 316
D. 324


Answer: C. 316


Solution:


Given,

a − b = 4, ab = 21

Then,

⇒ (a − b)3 = a3 − 3a2b + 3ab2 − b3 = a3 − 3ab(a − b) − b3

⇒ 43 = a3 − b3 − 3(21)(4)

⇒ 64 + 252 = a3 − b3

∴ a3 − b3 = 316


Hence, the answer a3 − b3 = 316.




Read more:


If a + b = 5 and ab = 6, find a^2 + b^2 .

Leave a Reply

Your email address will not be published.