What are the solutions to the equation abcx^2-(a^2b^2+c^2)x+abc=0 ?

The solutions to the equation abcx^2-(a^2b^2+c^2)x+abc=0 are

Find the zeros of abcx^2-(a^2b^2+c^2)x+abc=0

The zeros of abcx^2-(a^2b^2+c^2)x+abc=0 are

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ab c x^{2} - (a^{2} b^{2} + c^{2}) x + ab c = 0

x = \frac{a ^{2} b ^{2} + c ^{2} + a ^{4} b ^{4} - 2 a ^{2} b ^{2} c ^{2} + c ^{4}}{2 ab c}, x = \frac{a ^{2} b ^{2} + c ^{2} - a ^{4} b ^{4} - 2 a ^{2} b ^{2} c ^{2} + c ^{4}}{2 ab c}; ab c \neq = 0

Solution steps

ab c x^{2} - (a^{2} b^{2} + c^{2}) x + ab c = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - a ^{2} b ^{2} - c ^{2} ) \pm ( - a ^{2} b ^{2} - c ^{2} ) ^{2} - 4 ab c ab c}{2 ab c}

Simplify

(- a^{2} b^{2} - c^{2})^{2} - 4 ab c ab c : a^{4} b^{4} - 2 a^{2} b^{2} c^{2} + c^{4}

x_{1, 2} = \frac{- ( - a ^{2} b ^{2} - c ^{2} ) \pm a ^{4} b ^{4} - 2 a ^{2} b ^{2} c ^{2} + c ^{4}}{2 ab c}; ab c \neq = 0

Separate the solutions

x_{1} = \frac{- ( - a ^{2} b ^{2} - c ^{2} ) + a ^{4} b ^{4} - 2 a ^{2} b ^{2} c ^{2} + c ^{4}}{2 ab c}, x_{2} = \frac{- ( - a ^{2} b ^{2} - c ^{2} ) - a ^{4} b ^{4} - 2 a ^{2} b ^{2} c ^{2} + c ^{4}}{2 ab c}

x = \frac{- ( - a ^{2} b ^{2} - c ^{2} ) + a ^{4} b ^{4} - 2 a ^{2} b ^{2} c ^{2} + c ^{4}}{2 ab c} : \frac{a ^{2} b ^{2} + c ^{2} + a ^{4} b ^{4} - 2 a ^{2} b ^{2} c ^{2} + c ^{4}}{2 ab c}

x = \frac{- ( - a ^{2} b ^{2} - c ^{2} ) - a ^{4} b ^{4} - 2 a ^{2} b ^{2} c ^{2} + c ^{4}}{2 ab c} : \frac{a ^{2} b ^{2} + c ^{2} - a ^{4} b ^{4} - 2 a ^{2} b ^{2} c ^{2} + c ^{4}}{2 ab c}

The solutions to the quadratic equation are:

x = \frac{a ^{2} b ^{2} + c ^{2} + a ^{4} b ^{4} - 2 a ^{2} b ^{2} c ^{2} + c ^{4}}{2 ab c}, x = \frac{a ^{2} b ^{2} + c ^{2} - a ^{4} b ^{4} - 2 a ^{2} b ^{2} c ^{2} + c ^{4}}{2 ab c}; ab c \neq = 0

- 22 - 3 x^{2} - 2 x = - 3

- 3 x^{2} = 12

12 x^{2} - 24 = 0

9 p^{2} - 1 = 0

x^{2} - 4 x = 15

What are the solutions to the equation abcx^2-(a^2b^2+c^2)x+abc=0 ?
The solutions to the equation abcx^2-(a^2b^2+c^2)x+abc=0 are
Find the zeros of abcx^2-(a^2b^2+c^2)x+abc=0
The zeros of abcx^2-(a^2b^2+c^2)x+abc=0 are