If a, b,and c are in GP. prove that
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Step-by-step explanation:
We know that
If a,b,c are in the GP then b²=ac----(1)
LHS:-
a²b²c²(1/a³+1/b³+1/c³)
=>a²c²(ac)[(b³c³+a³c³+a³b³)/a³b³c³]
=>a³c³[(b³c³+a³c³+a³b³)/a³b³c³]
=>(b³c³+a³c³+a³b³)/b³
=>(b³c³/b³)+(a³c³/b³)+(a³b³/b³)
=>c³+[(ac)³/b³]+a³
=>a³+c³+[(b²)³/b³]
=>a³+c³+[b⁶/b³]
=>a³+c³+b³
=>a³+b³+c³
=>RHS
LHS=RHS
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