What are the solutions to the equation solvefor a,0=a^2-ab-b^2 ?

The solutions to the equation solvefor a,0=a^2-ab-b^2 are a=(b+sqrt(5)b)/2 ,a=(b-sqrt(5)b)/2

Find the zeros of solvefor a,0=a^2-ab-b^2

The zeros of solvefor a,0=a^2-ab-b^2 are a=(b+sqrt(5)b)/2 ,a=(b-sqrt(5)b)/2

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solve for

a, 0 = a^{2} - ab - b^{2}

a = \frac{b + 5 b}{2}, a = \frac{b - 5 b}{2}

Solution steps

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

Switch sides

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

Write in the standard form

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

a^{2} - ba - b^{2} = 0

Solve with the quadratic formula

a_{1, 2} = \frac{- ( - b ) \pm ( - b ) ^{2} - 4 \cdot 1 \cdot ( - b ^{2} )}{2 \cdot 1}

Simplify

(- b)^{2} - 4 \cdot 1 \cdot (- b^{2}) : 5 b

a_{1, 2} = \frac{- ( - b ) \pm 5 b}{2 \cdot 1}

Separate the solutions

a_{1} = \frac{- ( - b ) + 5 b}{2 \cdot 1}, a_{2} = \frac{- ( - b ) - 5 b}{2 \cdot 1}

a = \frac{- ( - b ) + 5 b}{2 \cdot 1} : \frac{b + 5 b}{2}

a = \frac{- ( - b ) - 5 b}{2 \cdot 1} : \frac{b - 5 b}{2}

The solutions to the quadratic equation are:

a = \frac{b + 5 b}{2}, a = \frac{b - 5 b}{2}

x^{2} = 25

- 4 x^{2} - 40 x = 164

- 4 x^{2} - 12 x - 5 = 0

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

y, 3 x^{2} + 2 x + 5 y^{2} - 7 y + 23 = 0

What are the solutions to the equation solvefor a,0=a^2-ab-b^2 ?
The solutions to the equation solvefor a,0=a^2-ab-b^2 are a=(b+sqrt(5)b)/2 ,a=(b-sqrt(5)b)/2
Find the zeros of solvefor a,0=a^2-ab-b^2
The zeros of solvefor a,0=a^2-ab-b^2 are a=(b+sqrt(5)b)/2 ,a=(b-sqrt(5)b)/2