The difference of square of two natural number is 84.The square of larger is 25 times the smaller part.Find the number
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Let the numbers be x and y
x^2-y^2=84,x^2=84+y^2
x^2=25y
From both we get
25y=84+y^2
y^2-25y+84=0
y^2-21y-4y+84=0
y(y-21)-4(y-21)=0
y-21=0 or y-4=0
If y=21
x^2=25*21=525 which is not a perfect square number
Hence, y=4
x^2=25*4=100
x=10,y=4
x^2-y^2=84,x^2=84+y^2
x^2=25y
From both we get
25y=84+y^2
y^2-25y+84=0
y^2-21y-4y+84=0
y(y-21)-4(y-21)=0
y-21=0 or y-4=0
If y=21
x^2=25*21=525 which is not a perfect square number
Hence, y=4
x^2=25*4=100
x=10,y=4
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