need help please!

[gomati]

let x>1,y>1 and (lnx)² +(lny)²= lnx² + lny², then find the maximum value of x^lny.
2. prove that ; 4 sin27⁰ = (5+5^1/2 )^1/2 -(3-5^1/2​).

 

[Deleted member 4993]

let x>1,y>1 and (lnx)² +(lny)²= lnx² + lny², then find the maximum value of x^lny.
2. prove that ; 4 sin27⁰ = (5+5^1/2 )^1/2 -(3-5^1/2​).

These are pretty interesting problems.

For the first one - I would start with substitution:A

lnx = m and lny = n

An interesting observation x^lny = y^lnx for all x,y >1

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

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