Solve y^10 + y^5 + 1

Question

Simplify the expression

Solution

y^{5} + 1

Evaluate

y \times 0 + y^{5} + 1

Any expression multiplied by 0 equals 0

0 + y^{5} + 1

Solution

y^{5} + 1

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Factor

(y + 1) (y^{4} - y^{3} + y^{2} - y + 1)

Evaluate

y \times 0 + y^{5} + 1

Any expression multiplied by 0 equals 0

0 + y^{5} + 1

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

y^{5} + 1

Calculate

y^{5} - y^{4} + y^{3} - y^{2} + y + y^{4} - y^{3} + y^{2} - y + 1

Rewrite the expression

y \times y^{4} - y \times y^{3} + y \times y^{2} - y \times y + y + y^{4} - y^{3} + y^{2} - y + 1

Factor out y from the expression

y (y^{4} - y^{3} + y^{2} - y + 1) + y^{4} - y^{3} + y^{2} - y + 1

Solution

(y + 1) (y^{4} - y^{3} + y^{2} - y + 1)

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Find the roots of the algebra expression

y = - 1

Evaluate

y^{1} \times 0 + y^{5} + 1

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

y^{1} \times 0 + y^{5} + 1 = 0

Evaluate the power

y \times 0 + y^{5} + 1 = 0

Any expression multiplied by 0 equals 0

0 + y^{5} + 1 = 0

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

y^{5} + 1 = 0

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

y^{5} = 0 - 1

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

y^{5} = - 1

Take the 5 -th root on both sides of the equation

5 y^{5} = 5 - 1

Calculate

y = 5 - 1

Solution

More Steps

Evaluate

5 - 1

An odd root of a negative radicand is always a negative

- 51

Simplify the radical expression

- 1

y = - 1

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