Question

If 'b' is the mean proportion between 'a' and 'c', prove that:
(a²-b²+c²)/(a-¹+b-²+c-²) = b⁴

Answer 1

Answer:

Since, b is the mean proportional between a and c. So b2 = ac.

L.H.S. = a2 – b2 + c2/a-2 – b-2 + c-2

= a2 – b2 + c2/1/a2 – 1/b2 + 1/c2

= (a2 – b2 + c2)/b2c2 – a2c2 + a2b2/a2b2c2

= a2b2c2 (a2 – b2 + c2)/b2c2 – b4 + a2b2

= b4 × b2(a2 – b2 + c2)/b2(c2 – b2 + a2)

b4 = R.H.S.

Hence proved.

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