Question

Solve each expression using the imaginary unit I.
71.sqrt-2-3




Solve each equation.
81.5x^2-2x+1=0




Solve each system by substitution
85.y=-x^2-7x-6
y=x^2-8x-12

Answer 1

@iGreen can you just help me with number 71?

Answer 2

??

Is it this?

\(\sqrt{-2} - 3\)

or

\(\sqrt{-2-3}\)

Answer 3

The first one.

Answer 4

Okay.

Answer 5

Wait, so do they like want it in decimal form or..?

Do you have choices?

Answer 6

Ugh, it wants me to simplify each expression. . No I don't, it's a study guide.

Answer 7

iGreen?

Answer 8

.\(\large\tt \begin{align} \color{black}{\sqrt{-2}-3\\~\\
}\end{align}\)

is this is it?

Answer 9

Yes

Answer 10

\(\large\tt \begin{align} \color{black}{\sqrt{-2}-3\\~\\
=\sqrt{2\times -1}-3\\~\\
=\sqrt{2}\times \sqrt{-1}-3\\~\\
=\sqrt{2}\times i-3-----------\color{blue}{(i=\sqrt{-1})}\\~\\
=\sqrt{2}i-3\\~\\}\end{align}\)

Answer 11

Thank you!

Answer 12

\(\large\tt \begin{align} \color{black}{5x^2-2x+1=0\\~\\
\\~\\}\end{align}\)

compare it with
\(\large\tt \begin{align} \color{black}{ax^2+bx+c=0\\
}\end{align}\)

so here
\(\large\tt \begin{align} \color{black}{a=5,b=-2,c=1}\end{align}\)

now apply formula

\(\large\tt \begin{align} \color{black}{x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\~\\
x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4\times 5\times 1}}{2\times 5}\\~\\
=\dfrac{2\pm \sqrt{-16}}{10}\\~\\
=\dfrac{2\pm \sqrt{16}\times \sqrt{-1}}{10}\\~\\
=\dfrac{2\pm 4\times i}{10}\\~\\
=\dfrac{1+ 2i}{5}~~or~~\dfrac{1- 2i}{5}}\end{align}\)

Answer 13

Thank you. xD

Answer 14

try the third