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Noah and Lin are each trying to solve the equation x² - 6x + 10 = 0. They know that the solutions to x² = - 1 are i and -i, but they are not sure how to use this information to solve for x in their equation.

Here is Noah's work:
x² - 6x + 10 = 0
x² - 6x = -10
x² - 6x + 9 = -10 + 9
(x-3)² = -1

Show how Noah can finish his work using complex numbers.​

Respuesta :

absor201

Answer:

Solving the equation [tex]x^2 - 6x + 10 = 0[/tex] we get [tex]x=3+i \ , \ x=3-i[/tex]

Step-by-step explanation:

Noah's step to solve the equation [tex]x^2 - 6x + 10 = 0[/tex] are:

[tex]x^2 - 6x + 10 = 0\\x^2 - 6x = -10\\x^2 - 6x + 9 = -10 + 9\\(x-3)^2 = -1[/tex]

The next step is to take square root on both sides because: [tex]\sqrt{x^2}=x[/tex]

[tex]\sqrt{(x-3)^2}=\sqrt{-1} \\x-3=\pm\sqrt{-1} \\x=\pm(\sqrt{-1})+3 \\[/tex]

Now, we know that: [tex]\sqrt{-1}=i[/tex]

[tex]x=\pm(i)+3\\x=3+i \ , \ x=3-i[/tex]

So, Solving the equation [tex]x^2 - 6x + 10 = 0[/tex] we get [tex]x=3+i \ , \ x=3-i[/tex]

The steps for Noah finishing his work have been shown below and the solution is;

x = 3 + i and x = 3 - i

Noah's work is;

x² - 6x + 10 = 0

x² - 6x = -10

x² - 6x + 9 = -10 + 9

(x - 3)² = -1

Now, the next step would be to take the square root of both sides to obtain;

x - 3 = √(-1)

Now, we are told that the solution to x² = -1 are i and -i. Now, x² = -1 can also be written as;

x = √(-1)

Thus, the solution to x = √(-1) is i and -i.

Thus;

x - 3 = i and x - 3 = -i

Thus;

x = 3 + i and x = 3 - i

Read more at; https://brainly.com/question/21017545

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