Question

x^2 + y^2 = 7x then prove that 2 log ( x + y) = log x + log y+ 2 log 3

Answer 1

HEYA!!!!

Here is your answer Rehan Bhai :
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${x}^{2} + {y}^{2} = 7xy\\ \\ add \: 2xy \: on \: both \: sides \\ \\ {x}^{2} + {y}^{2} + 2xy = 7xy+ 2xy \\ \\ {(x + y)}^{2} = 9xy \\ \\ add \: log \: on \: both \: sides \\ log {(x + y)}^{2} = log \: 9xy \\ \\ 2 \: log(x + y) = log \: {3}^{2} + log \: x + log \: y \\ \\ 2 \: log \: \: (x + y) = 2 \: log3 + log \: x \: log \: y$

HOPE THIS HELPS U...

Answer 2

Hi ,

x² + y² = 7xy ( given )

add 2xy both sides of the equation

x² + y² + 2xy = 7xy + 2xy

( x + y )² = 9xy

Take log both sides of the equation,

log ( x + y )² = log 9xy

2 log ( x+ y ) = log 9 + log x + logy

= log 3² + log x + log y

= 2 log 3 + log x + log y

Therefore ,

2 log ( x + y ) = log x + log y + 2 log 3

Hence proved.

I hope this helps you.

: )