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dedylja [7]
3 years ago
6

If c is a real number and if 1 + i is a solution of the equation x^2 -2x + c = 0, what is the value of c?

Mathematics
2 answers:
Nana76 [90]3 years ago
6 0

Answer:

c = 2

Step-by-step explanation:

Substitute x = 1 + i into the equation

(1 + i)² - 2(1 + i) + c = 0 ← distribute left side

1 + 2i + i² - 2 - 2i + c = 0 ( note that i² = - 1 )

1 + 2i - 1 - 2 - 2i + c = 0 ← collect like terms on left

- 2 + c = 0 ( add 2 to both sides )

c = 2

Mekhanik [1.2K]3 years ago
6 0

Answer:

c = 2.

Step-by-step explanation:

Complex solutions come in conjugate pairs so the other solution is 1 - i.

So we have:

(x - (1 + i)(x - (1 - i) = 0

(x - 1 - i)(x - 1 + i) = 0

x^2 - x + ix - x + 1 - i  -ix  +i - i^2 = 0

x^2  -2x  + 1 - i^2 = 0

x^2 - 2x + 1 + 1 = 0

x^2 - 2x + 2 = 0

c = 2.

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Answer:

YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

Step-by-step explanation:

Given

Given that the function f(x) and g(x) are inverse functions.

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g(x) = 3x - 15

To determine

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<u>Determining the inverse function of f(x) </u>

A function g is the inverse function of f if for y = f(x), x = g(y)

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Solve for y

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Therefore,

YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

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