Question

If x² + y² = 23 xy the prove that 2 log ( x+ y) = 2 log 5+log x+ log y

Answer 1

Answer:

Given:

x

2

+y

2

=23xy,

So, the above equation can be written as

x

2

+y

2

=25xy−2xy

x

2

+y

2

+2xy=25xy

(x+y)

2

=25xy

(x+y)

2

/25=xy

Now by taking log on both sides, we get

log[(x+y)

2

]/25=logxy

log[(x+y)/5]

2

=logx+logy

2log[(x+y)/5]=logx+logy

log(x+y)/5=1/2(logx+logy)

Hence proved