Solve a^563-a - ScanMath

Question

Simplify the expression

63 a^{5} - a

Evaluate

a^{5} \times 63 - a

Solution

63 a^{5} - a

Show Solution

a (63 a^{4} - 1)

Evaluate

a^{5} \times 63 - a

Use the commutative property to reorder the terms

63 a^{5} - a

Rewrite the expression

a \times 63 a^{4} - a

Solution

a (63 a^{4} - 1)

Show Solution

a_{1} = - \frac{4 6 3 ^{3}}{63}, a_{2} = 0, a_{3} = \frac{4 6 3 ^{3}}{63}

Alternative Form

a_{1} \approx - 0.354948, a_{2} = 0, a_{3} \approx 0.354948

Evaluate

a^{5} \times 63 - a

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

a^{5} \times 63 - a = 0

Use the commutative property to reorder the terms

63 a^{5} - a = 0

Factor the expression

a (63 a^{4} - 1) = 0

Separate the equation into 2 possible cases

a = 0 63 a^{4} - 1 = 0

Solve the equation

More Steps

Evaluate

63 a^{4} - 1 = 0

Move the constant to the right-hand side and change its sign

63 a^{4} = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

63 a^{4} = 1

Divide both sides

\frac{63 a ^{4}}{63} = \frac{1}{63}

Divide the numbers

a^{4} = \frac{1}{63}

Take the root of both sides of the equation and remember to use both positive and negative roots

a = \pm 4 \frac{1}{63}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{63}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 1}{4 63}

Simplify the radical expression

\frac{1}{4 63}

Multiply by the Conjugate

\frac{4 6 3 ^{3}}{4 63 \times 4 6 3 ^{3}}

Multiply the numbers

\frac{4 6 3 ^{3}}{63}

a = \pm \frac{4 6 3 ^{3}}{63}

Separate the equation into 2 possible cases

a = \frac{4 6 3 ^{3}}{63} a = - \frac{4 6 3 ^{3}}{63}

a = 0 a = \frac{4 6 3 ^{3}}{63} a = - \frac{4 6 3 ^{3}}{63}

Solution

a_{1} = - \frac{4 6 3 ^{3}}{63}, a_{2} = 0, a_{3} = \frac{4 6 3 ^{3}}{63}

Alternative Form

a_{1} \approx - 0.354948, a_{2} = 0, a_{3} \approx 0.354948

Show Solution