Advertisements
Advertisements
Question
ab = 36, a − b = 9 ∴ a3 − b3 = ______.
Options
243
1701
729
765
MCQ
Fill in the Blanks
Advertisements
Solution
ab = 36, a − b = 9 ∴ a3 − b3 = 1701.
Explanation:
a3 − b3 = (a − b) (c)
Let’s find a2 + b2:
a2 + b2 = (a − b)2 + 2ab
a2 + b2 = (9)2 + 2(36)
a2 + b2 = 81 + 72
a2 + b2 = 153
Then,
a2 + ab + b2 = a2 + b2 + ab
= 153 + 36
= 189
Hence,
a3 − b3 = 9 × 189
a3 − b3 = 1701
shaalaa.com
Is there an error in this question or solution?
