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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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Since, b is the mean proportional between a and c. So b2 = ac.
L.H.S. a2b2+ c2/a-2-b-2+ c-2 = =a2b2+ c2/1/a2 - 1/b2 + 1/c2
= (a2b2+ c2)/b2c2a2c2 + a2b2/ a2b2c2
= a2b2c2 (a2-b2+ c2)/b2c2 - b4 +
a2b2
= b4 × b2(a2b2+ c2)/b2(c2-b2+ a2)
b4 = R.H.S.
Hence proved
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