ProofHard3 marks
If x/a = y/b = z/c, show that (x³ / a³) + (y³ / b³) + (z³ / c³) = 3xyz/abc
Topic: Recurring deposit / interest
Previous-year question practice database
Answer
Exam answer
Given:
x/a = y/b = z/c = k
Therefore:
x = ak y = bk z = ck
Left-hand side:
x³/a³ + y³/b³ + z³/c³
= (ak)³/a³ + (bk)³/b³ + (ck)³/c³
= k³ + k³ + k³
= 3k³
Right-hand side:
3xyz/(abc)
= 3(ak)(bk)(ck)/(abc)
= 3k³
Therefore:
Left-hand side = Right-hand side.
Hence proved.
Explanation
Introduce a common ratio k. Substituting x = ak, y = bk and z = ck reduces both sides independently to 3k³.
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