Question

Please HELP ME!!!

$x=1+i$ is a solution to which of the following equations?

a: $x^{2}+1=0$
b:$x^{2} -2x+2=0$
c: $x^{2} -2x+1=0$
d:$x^{2} -1=0$

If you could please share you're thought process and work with me as well, so I can better understand how you found the answer. Thanks a bunch!

Answer 1

Answer:

• b. x² - 2x + 2 = 0

Step-by-step explanation:

Solve each to confirm answer

a.

• x² + 1 = 0
• x² = - 1
• x = √ -1
• x = i

• FALSE

b.

• x² - 2x + 2 = 0
• (x - 1)² + 1 = 0
• (x - 1)² = - 1
• x - 1 = √-1
• x - 1 = i
• x = 1 + i

• TRUE

c.

• x² - 2x + 1 = 0
• (x - 1)² = 0
• x - 1 = 0
• x = 1

• FALSE

d.

• x² - 1 = 0
• x² = 1
• x = √1
• x = ± 1

• FALSE

Answer 2

Answer:

Option B

Step-by-step explanation:

$\\ \sf\longmapsto x^2-2x+2=0$

$\\ \sf\longmapsto x=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(2)}}{2(1)}$

$\\ \sf\longmapsto x=\dfrac{2\pm\sqrt{4-8}}{2}$

$\\ \sf\longmapsto x=\dfrac{2\pm\sqrt{-4}}{2}$

$\\ \sf\longmapsto x=\dfrac{2\pm 2i}{2}$

$\\ \sf\longmapsto x=1\pm i$

Verified