10/x^2-1/y=1/5

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Solution for 10/x^2-1/y=1/5 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

10/(x^2)-(1/y) = 1/5 // - 1/5

10/(x^2)-(1/y)-(1/5) = 0

10/(x^2)-y^-1-1/5 = 0

10*x^-2 = -(-y^-1-1/5) // : 10

x^-2 = (y^-1+1/5)/10

-2 < 0

1/(x^2) = (y^-1+1/5)/10 // * x^2

1 = x^2*((y^-1+1/5)/10) // : (y^-1+1/5)/10

10*(y^-1+1/5)^-1 = x^2

x^2 = 10*(y^-1+1/5)^-1 // ^ 1/2

abs(x) = 10^(1/2)*(y^-1+1/5)^(-1/2)

x = 10^(1/2)*(y^-1+1/5)^(-1/2) or x = -(10^(1/2)*(y^-1+1/5)^(-1/2))

x in { 10^(1/2)*(y^-1+1/5)^(-1/2), -(10^(1/2)*(y^-1+1/5)^(-1/2)) }

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