If x=3–√−1, what is the value of (x2+2x−2) ? A −(3^(1/2)) B 0 C 3^(1/2) D 3

Substitute x value: Substitute the value of x into the expression. x = 3 - √(-1), so we substitute this into the expression x^2 + 2x - 2. (3 - √(-1))^2 + 2(3 - √(-1)) - 2Simplify by squaring: Simplify the expression by squaring x. (3 - √(-1))^2 = 3^2 - 2(3)(√(-1)) + (√(-1))^2 = 9 - 6√(-1) - 1 = 8 - 6√(-1)Multiply and simplify: Multiply 2 by x and simplify. 2(3 - √(-1)) = 6 - 2√(-1)Combine and subtract: Combine the results from Step 2 and Step 3 and subtract 2. (8 - 6√(-1)) + (6 - 2√(-1)) - 2 = 8 + 6 - 2 - 6√(-1) - 2√(-1) = 12 - 8 - 8√(-1) = 4 - 8√(-1)

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If $x=3-\sqrt{-1}$ , what is the value of $(x^2+2x-2)$ ? $\newline$ (A) $-3^{(1/2)}$ $\newline$ (B) $0$ $\newline$ (C) $3^{(1/2)}$ $\newline$ (D) $3$

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Math Problems

Algebra 1

Transformations of quadratic functions

Full solution

Q. If

x=3-\sqrt{-1}

, what is the value of

(x^2+2x-2)

\newline

(A)

-3^{(1/2)}

\newline

(B)

0

\newline

(C)

3^{(1/2)}

\newline

(D)

3

Substitute x value: Substitute the value of $x$ into the expression. $\newline$ $x = 3 - \sqrt{-1}$ , so we substitute this into the expression $x^2 + 2x - 2$ . $\newline$ $(3 - \sqrt{-1})^2 + 2(3 - \sqrt{-1}) - 2$
Simplify by squaring: Simplify the expression by squaring $x$ . $(3 - \sqrt{-1})^2 = 3^2 - 2(3)(\sqrt{-1}) + (\sqrt{-1})^2 = 9 - 6\sqrt{-1} - 1 = 8 - 6\sqrt{-1}$
Multiply and simplify: Multiply $2$ by $x$ and simplify. $2(3 - \sqrt{-1}) = 6 - 2\sqrt{-1}$
Combine and subtract: Combine the results from Step $2$ and Step $3$ and subtract $2$ . $\newline$ $(8 - 6\sqrt{-1}) + (6 - 2\sqrt{-1}) - 2$ $\newline$ $= 8 + 6 - 2 - 6\sqrt{-1} - 2\sqrt{-1}$ $\newline$ $= 12 - 8\sqrt{-1}$ $\newline$ $= 4 - 8\sqrt{-1}$