What are the solutions to the equation abx^2+ab=a^2x+b^2x ?

The solutions to the equation abx^2+ab=a^2x+b^2x are x= a/b ,x= b/a ;\quad ab\ne 0

Find the zeros of abx^2+ab=a^2x+b^2x

The zeros of abx^2+ab=a^2x+b^2x are x= a/b ,x= b/a ;\quad ab\ne 0

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ab x^{2} + ab = a^{2} x + b^{2} x

x = \frac{a}{b}, x = \frac{b}{a}; ab \neq = 0

Solution steps

ab x^{2} + ab = a^{2} x + b^{2} x

Move

b^{2} x

to the left side

ab x^{2} + ab - b^{2} x = a^{2} x

Move

a^{2} x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

Simplify

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = \frac{a}{b}, x = \frac{b}{a}; ab \neq = 0

x^{2} + 6 x = - 8

12 x^{2} - 19 x + 5 = 0

0 = 0.25 x^{2} - x + 1

(13.5 + 0.75 x) \cdot x = - 24

- 3 x^{2} - 54 x + 51 = 0

What are the solutions to the equation abx^2+ab=a^2x+b^2x ?
The solutions to the equation abx^2+ab=a^2x+b^2x are x= a/b ,x= b/a ;\quad ab\ne 0
Find the zeros of abx^2+ab=a^2x+b^2x
The zeros of abx^2+ab=a^2x+b^2x are x= a/b ,x= b/a ;\quad ab\ne 0