Question

X2+y2=119xy then s.t 2log11+logx+logy

Answer 1

Step-by-step explanation:

Given Question:-

X2+y2=119xy then s.t 2log11+logx+logy

Correct Question:-

If x^2+y^2 = 119xy then show that

2log(x+y) = 2 log 11 + log x + log y

Solution:-

Given that :

x^2+y^2 = 119xy

On adding 2xy both sides then

x^2+y^2+2xy = 119xy+2xy

=> x^2+y^2+2xy = 121 xy

=> (x+y)^2 = 121 xy

( Since (a+b)^2 = a^2+2ab+b^2,

Where ,a = x and b = y )

On taking logarithms both sides then

=> log (x+y)^2 = log 121 xy

=> log (x+y)^2 = log ( 11×11×x×y)

=> log (x+y)^2 = log ( 11^2×x×y)

We know that

log ab = log a + log b

=> log (x+y)^2 = log 11^2 + log x + log y

We know that

log a^m = m log a

=> 2 log (x+y) = 2 log 11 + log x + log y

Hence , Proved.

Used formulae:-

• (a+b)^2 = a^2+2ab+b^2

• log ab = log a + log b

• log a^m = m log a