If 'b' is the mean proportion between 'a' and 'c', prove that:(a²-b²

1.	If 'b' is the mean proportion between 'a' and 'c', prove that:(a²-b²+c²)/(a-¹+b-²+c-²) = b⁴
Answer» 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. *PLEASE* *MARK* ME AS *BRAINLIST*

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

Answer»

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

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