What are the solutions to the equation (m^2-n^2)x^2-4mnx=m^2-n^2 ?

The solutions to the equation (m^2-n^2)x^2-4mnx=m^2-n^2 are

Find the zeros of (m^2-n^2)x^2-4mnx=m^2-n^2

The zeros of (m^2-n^2)x^2-4mnx=m^2-n^2 are

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(m^{2} - n^{2}) x^{2} - 4 mn x = m^{2} - n^{2}

x = \frac{2 mn + 4 m ^{2} n ^{2} - ( m ^{2} - n ^{2} ) ( n ^{2} - m ^{2} ) ^{2}}{m ^{2} - n ^{2}}, x = \frac{2 mn - 4 m ^{2} n ^{2} - ( m ^{2} - n ^{2} ) ( n ^{2} - m ^{2} ) ^{2}}{m ^{2} - n ^{2}}; m^{2} - n^{2} \neq = 0

Solution steps

(m^{2} - n^{2}) x^{2} - 4 mn x = m^{2} - n^{2}

Move

n^{2}

to the left side

(m^{2} - n^{2}) x^{2} - 4 mn x + n^{2} = m^{2}

Move

m^{2}

to the left side

(m^{2} - n^{2}) x^{2} - 4 mn x + n^{2} - m^{2} = 0

Solve with the quadratic formula

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

Simplify

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

x_{1, 2} = \frac{- ( - 4 mn ) \pm 2 4 m ^{2} n ^{2} - ( m ^{2} - n ^{2} ) ( - m ^{2} + n ^{2} ) ^{2}}{2 ( m ^{2} - n ^{2} )}; m^{2} - n^{2} \neq = 0

Separate the solutions

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

x = \frac{- ( - 4 mn ) + 2 4 m ^{2} n ^{2} - ( m ^{2} - n ^{2} ) ( - m ^{2} + n ^{2} ) ^{2}}{2 ( m ^{2} - n ^{2} )} : \frac{2 mn + 4 m ^{2} n ^{2} - ( m ^{2} - n ^{2} ) ( n ^{2} - m ^{2} ) ^{2}}{m ^{2} - n ^{2}}

x = \frac{- ( - 4 mn ) - 2 4 m ^{2} n ^{2} - ( m ^{2} - n ^{2} ) ( - m ^{2} + n ^{2} ) ^{2}}{2 ( m ^{2} - n ^{2} )} : \frac{2 mn - 4 m ^{2} n ^{2} - ( m ^{2} - n ^{2} ) ( n ^{2} - m ^{2} ) ^{2}}{m ^{2} - n ^{2}}

The solutions to the quadratic equation are:

x = \frac{2 mn + 4 m ^{2} n ^{2} - ( m ^{2} - n ^{2} ) ( n ^{2} - m ^{2} ) ^{2}}{m ^{2} - n ^{2}}, x = \frac{2 mn - 4 m ^{2} n ^{2} - ( m ^{2} - n ^{2} ) ( n ^{2} - m ^{2} ) ^{2}}{m ^{2} - n ^{2}}; m^{2} - n^{2} \neq = 0

\frac{2 x ^{2} + 7 x - 21}{16} - \frac{x ^{2} - 3}{4} = x

- 3 x^{2} + x + 1 = 0

- w^{2} + 6 w + 72 = 0

n C^{2} = 15

x^{2} - 12 = 13

What are the solutions to the equation (m^2-n^2)x^2-4mnx=m^2-n^2 ?
The solutions to the equation (m^2-n^2)x^2-4mnx=m^2-n^2 are
Find the zeros of (m^2-n^2)x^2-4mnx=m^2-n^2
The zeros of (m^2-n^2)x^2-4mnx=m^2-n^2 are