Given: (x-y)(x+y) = 2y(49x-y) ; x0 and y0Prove (x+y)^2 = 100xy

Question

Given: (x-y)(x+y) = 2y(49x-y) ; x>0 and y>0Prove (x+y)^2 = 100xy

Robert · Accepted Answer

Given: (x-y)(x+y) = 2y(49x-y) ; x>0 and y>0 
To prove (x+y)2 = 100xy 
Solution Statement 
x2 - y2 = 98xy -2y2  
x2 + y2 = 98xy 
We know that  
(x+y)^2 = x2 + y2 + 2xy 
Substituting the value of x2 + y2 = 98xy 
We get (x+y)^2 = 98xy + 2xy 
Hence Proved (x+y)^2 = 100xy

Given: (x-y)(x+y) = 2y(49x-y) ; x>0 and y>0 Prove (x+y)^2 = 100xy

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