Question

If b is the mean proportion between a and c, show that:
at + a^4 + a^2b^2 + b²/b^4 +b^2c^2 + c^4 = a^2/c^2

[Hint : Substitute 62 = ac in L.H.S. to get R.H.S.]

you will be reported for nonsense answer. ​

Answer 1

Step-by-step explanation:

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