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y=root(3)(x^(2)+x+1)

$y=\sqrt[3]{x^{2}+x+1}$

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Quadratic equation with complex roots

Full solution

Q.

y=\sqrt[3]{x^{2}+x+1}

Understand the problem: Understand the problem. $\newline$ We need to find the cube root of the expression $x^{2} + x + 1$ .
Write down the expression: Write down the expression for the cube root. $\newline$ The cube root of $x^{2} + x + 1$ is written as $y = \sqrt[3]{x^{2} + x + 1}$ .
Check for simplification: Check if the expression inside the cube root can be simplified. $\newline$ The expression $x^{2} + x + 1$ does not factor nicely, and there are no obvious simplifications, so we leave it as is under the cube root.
Express in radical form: Express the cube root in radical form. $\newline$ The cube root of $x^{2} + x + 1$ is written as $y = \sqrt[3]{x^{2} + x + 1}$ , which is already in its simplest radical form.
Ensure correct form: Ensure that the expression is in the correct form to answer the question prompt. $\newline$ The question prompt asks for the cube root of the expression $x^{2} + x + 1$ , and we have expressed $y$ as exactly that.

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