What are the solutions to the equation mnx^2+mn=x(m^2+n^2) ?

The solutions to the equation mnx^2+mn=x(m^2+n^2) are x= m/n ,x= n/m ;\quad mn\ne 0

Find the zeros of mnx^2+mn=x(m^2+n^2)

The zeros of mnx^2+mn=x(m^2+n^2) are x= m/n ,x= n/m ;\quad mn\ne 0

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mn x^{2} + mn = x (m^{2} + n^{2})

x = \frac{m}{n}, x = \frac{n}{m}; mn \neq = 0

Solution steps

mn x^{2} + mn = x (m^{2} + n^{2})

Move

x (m^{2} + n^{2})

to the left side

mn x^{2} + mn - x (m^{2} + n^{2}) = 0

Write in the standard form

a x^{2} + b x + c = 0

mn x^{2} - (m^{2} + n^{2}) x + mn = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - m ^{2} - n ^{2} ) \pm ( - m ^{2} - n ^{2} ) ^{2} - 4 mnmn}{2 mn}

Simplify

(- m^{2} - n^{2})^{2} - 4 mnmn : (m + n) (m - n)

x_{1, 2} = \frac{- ( - m ^{2} - n ^{2} ) \pm ( m + n ) ( m - n )}{2 mn}; mn \neq = 0

Separate the solutions

x_{1} = \frac{- ( - m ^{2} - n ^{2} ) + ( m + n ) ( m - n )}{2 mn}, x_{2} = \frac{- ( - m ^{2} - n ^{2} ) - ( m + n ) ( m - n )}{2 mn}

x = \frac{- ( - m ^{2} - n ^{2} ) + ( m + n ) ( m - n )}{2 mn} : \frac{m}{n}

x = \frac{- ( - m ^{2} - n ^{2} ) - ( m + n ) ( m - n )}{2 mn} : \frac{n}{m}

The solutions to the quadratic equation are:

x = \frac{m}{n}, x = \frac{n}{m}; mn \neq = 0

x^{2} - 26 x + 153 = 0

x^{2} - 5 x = 104

(z + 1)^{3} = z^{3}

6 x^{2} - 19 - 2 x = - 3 - 2 x + 5 x^{2}

\frac{b - 2 x ^{2}}{a} = m

What are the solutions to the equation mnx^2+mn=x(m^2+n^2) ?
The solutions to the equation mnx^2+mn=x(m^2+n^2) are x= m/n ,x= n/m ;\quad mn\ne 0
Find the zeros of mnx^2+mn=x(m^2+n^2)
The zeros of mnx^2+mn=x(m^2+n^2) are x= m/n ,x= n/m ;\quad mn\ne 0