x^1/2+x^-1/2=63x^-1

Solution for x^1/2+x^-1/2=63x^-1 equation:

D( x )

x = 0

x = 0

x = 0

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

(x^1)/2+(x^-1)/2 = 63*x^-1 // - 63*x^-1

(x^1)/2+(x^-1)/2-(63*x^-1) = 0

x/2+(x^-1)/2-63*x^-1 = 0

1/2*x^1-125/2*x^-1 = 0

(1/2*x^2-125/2*x^0)/(x^1) = 0 // * x^2

x^1*(1/2*x^2-125/2*x^0) = 0

x^1

(1/2)*x^2-125/2 = 0

(1/2)*x^2-125/2 = 0

DELTA = 0^2-(4*(1/2)*(-125/2))

DELTA = 125

DELTA > 0

x = (125^(1/2)+0)/(2*(1/2)) or x = (0-125^(1/2))/(2*(1/2))

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

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

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