If a,b,c,d are in continued properties, prove that \frac{(a-b)^{3}}{(b-c)^{3}

ruigE

ruigE

Answered question

2021-08-18

If a,b,c,d are in continued properties, prove that
(ab)3(bc)3=ad

Answer & Explanation

broliY

broliY

Skilled2021-08-19Added 97 answers

Step 1
a,b,c,d are in continued proportion
Therefore, we have
ab=bc=cd=k(say)
c=dk, b=ck=dk2, a=bk=dk3
Step 2
Consider,
(ab)3(bc)3=(dk3dk2)3(dk2dk)3
=d3k6(k1)d3k3(k1)
=k3
ad=dk3d=k3
Hence, (ab)3(bc)3=ad

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