If p - 2q = 3 and pq = 5, then what is the value of (p3 - 8q3)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 117
Given :
p - 2q = 3 and pq = 5
Formula used :
(a - b)3 = a3 - b3 - 3ab(a - b) ------ (1)
Calculations :
Using equation (1)
⇒ (p - 2q)3 = p3 - 8q3 -3(p)(2q)[p - 2q]
⇒ 33 = p3 - 8q3 - 6pq(3)
⇒ p3 - 8q3 = 27 + 90
⇒ 117