Solve (x-5)(x^5)-(x-6)(x^6) - ScanMath

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Question

Simplify the expression

7 x^{6} - 5 x^{5} - x^{7}

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Factor the expression

x^{5} (7 x - 5 - x^{2})

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{7 - 29}{2}, x_{3} = \frac{7 + 29}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 0.807418, x_{3} \approx 6.192582

Evaluate

(x - 5) (x^{5}) - (x - 6) (x^{6})

To find the roots of the expression,set the expression equal to 0

(x - 5) (x^{5}) - (x - 6) (x^{6}) = 0

Calculate

(x - 5) x^{5} - (x - 6) (x^{6}) = 0

Calculate

(x - 5) x^{5} - (x - 6) x^{6} = 0

Multiply the terms

x^{5} (x - 5) - (x - 6) x^{6} = 0

Multiply the terms

x^{5} (x - 5) - x^{6} (x - 6) = 0

Calculate

More Steps

7 x^{6} - 5 x^{5} - x^{7} = 0

Factor the expression

x^{5} (7 x - 5 - x^{2}) = 0

Separate the equation into 2 possible cases

x^{5} = 0 7 x - 5 - x^{2} = 0

The only way a power can be 0 is when the base equals 0

x = 0 7 x - 5 - x^{2} = 0

Solve the equation

More Steps

x = 0 x = \frac{7 + 29}{2} x = \frac{7 - 29}{2}

Solution

x_{1} = 0, x_{2} = \frac{7 - 29}{2}, x_{3} = \frac{7 + 29}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 0.807418, x_{3} \approx 6.192582

Show Solution