Question

if x^2 +y^2 - 2xy = 0 then find the value of log (x+y) base xy




please explain me .... soon​

Answer 1

Answer:

When x=0, we have

log(0+y)−2×0×y=0

⇒logy=0

⇒y=e

0

=1

Given equation is

log(x+y)−2xy=0

On differentiating w,r,t x we get

x+y

1

(1+

dx

dy

)−2y−2x

dx

dy

=0

On putting x=0,y=1 we get

(1+

dx

dy

)−2−0=0

⇒(1+

dx

dy

)−2=0

⇒

dx

dy

=1

ie,y

′

(x)=1

⇒y

′

(0)=1