a power x = b power y = c power z and b square = ac. Prove y = 2xz/ x + y
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aditya1557272827:
ready the questin carefully...u have to prove something
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4th line is wrong
no problem....i got the method
Answered by
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Hi ,
It is given that ,
a^x = b^y = c^z ---( 1 )
b² = ac ---( 2 )
Let us assume ,
a^x = b^y = c^z = k
1 ) a^x = k ,
a = k^1/x ---( 3 )
similarly ,
2 ) b = k^1/y ---( 4 )
3 ) c = k^1/z ---( 5 )
from ( 2 ) ,
b² = ac
( k^1/y )² = ( k^1/x ) ( k^1/z ) [ from ( 3 ),(4),(5 ) ]
k^2/y = k ^1/x+1/z
2/y = 1/x + 1/z
2/y = ( z + x )/xz
y/2 = xz/( z + x )
y = 2xz/( x + z )
Hence proved.
I hope this helps you.
: )
It is given that ,
a^x = b^y = c^z ---( 1 )
b² = ac ---( 2 )
Let us assume ,
a^x = b^y = c^z = k
1 ) a^x = k ,
a = k^1/x ---( 3 )
similarly ,
2 ) b = k^1/y ---( 4 )
3 ) c = k^1/z ---( 5 )
from ( 2 ) ,
b² = ac
( k^1/y )² = ( k^1/x ) ( k^1/z ) [ from ( 3 ),(4),(5 ) ]
k^2/y = k ^1/x+1/z
2/y = 1/x + 1/z
2/y = ( z + x )/xz
y/2 = xz/( z + x )
y = 2xz/( x + z )
Hence proved.
I hope this helps you.
: )
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