Question

Given that a to the power X = b to the power y = c to the power Z and b square = ac. Prove that 1 by X + 1 by Z = 2 by y

Please answer this in a picture or do the full maths process.. This is really urgent

Answer 1

Hi ,

It is given that ,

a^x = b^y = c^z

Let a^x = b^y = c^z = k

1 ) a^x = k implies a = k^1/x

2 ) b^y = k implies b = k^1/y

3 ) c^z = k implies c = k^1/z


Now ,

b² = ac [ given ]

( k^1/y )² = ( k^1/x ) ( k^1/z )

k^2/y = k^( 1/x + 1/y )

[ Since i ) ( a^m )ⁿ = a^mn

ii ) a^m × a^n = a^ m+n ]

2/y = 1/x + 1/z

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Since ,

If a^m = a^n then m = n

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Therefore ,

1/x + 1/z = 2/y

I hope this helps you.

: )