Given x >0, y >0.2009x2=2010y2, under the root sign (2009x+2010y)= under the root sign 2009+ under the root sign 2010. Find the value of one x + one y

X >0y >0 2009X^2=2010y^22009/2010=y^2/x^2√2009x=√2010y√2009/√2010=y/x from known√(2009x+2010y)=√2009+√2010, divided by √2010√[(2009x/2010)+y ]=√(2009/2010)+1√[(y^2/x)+y ]=y/x+1√[ y (x+y)/x ]=(x+y)/...

X >0, y >0,2009x squared =2010y squared, root number 2009x+2010y = root number 2009+ root number 2010, find 1/x+1/y

X >0y >0 2009X^2=2010y^2
2009/2010=Y^2/x^2
√2009 X =√2010y
√2009/√2010=Y/x
Given √(2009x+2010y)=√2009+√2010, both sides of the equation are divided by √2010
√[(2009X/2010)+ y ]=√(2009/2010)+1
√[(Y^2/x)+ y ]= y/x+1
√[ Y (x+y)/x ]=(x+y)/x
√Y =√(x+y)/x
Y=(x+y)/x
(X+y)/xy=1
1/X+1/y=1

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