Y/x=x/a

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Solution for Y/x=x/a equation:


D( x )

x = 0

x = 0

x = 0

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

Y/x = x/a // - x/a

Y/x-(x/a) = 0

Y*x^-1-(a^-1*x) = 0

t_1 = x^-1

Y*t_1^1-a^-1*t_1^-1 = 0

Y*t_1-(a^-1*t_1^-1) = 0

t_1^-1*(Y*t_1^2-a^-1) = 0

Y*t_1^2 = a^-1 // : Y

t_1^2 = (a^-1)/Y

t_1^2 = (a^-1)/Y // ^ 1/2

abs(t_1) = (a^(-1/2))/(Y^(1/2))

t_1 = (a^(-1/2))/(Y^(1/2)) or t_1 = -((a^(-1/2))/(Y^(1/2)))

1/t_1 = 0

1*t_1^-1 = 0 // : 1

t_1^-1 = 0

t_1 należy do O

t_1 = (a^(-1/2))/(Y^(1/2))

x^-1-((a^(-1/2))/(Y^(1/2))) = 0

1*x^-1 = Y^(-1/2)*a^(-1/2) // : 1

x^-1 = Y^(-1/2)*a^(-1/2)

-1 < 0

1/(x^1) = Y^(-1/2)*a^(-1/2) // * x^1

1 = Y^(-1/2)*a^(-1/2)*x^1 // : Y^(-1/2)*a^(-1/2)

1/(Y^(-1/2)*a^(-1/2)) = x^1

x = 1/(Y^(-1/2)*a^(-1/2))

t_1 = -((a^(-1/2))/(Y^(1/2)))

(a^(-1/2))/(Y^(1/2))+x^-1 = 0

1*x^-1 = -(Y^(-1/2)*a^(-1/2)) // : 1

x^-1 = -(Y^(-1/2)*a^(-1/2))

-1 < 0

1/(x^1) = -(Y^(-1/2)*a^(-1/2)) // * x^1

1 = -Y^(-1/2)*(-a^(-1/2))*x^1 // : -(Y^(-1/2)*a^(-1/2))

1/(-(Y^(-1/2)*a^(-1/2))) = x^1

x = 1/(-(Y^(-1/2)*a^(-1/2)))

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

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