What is the answer to x3+2x2+5six=1 ?

The answer to x3+2x2+5six=1 is s=0,x= 1/7

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x3+2x2+5six=1

x 3 + 2 x 2 + 5 s i x = 1

s = 0, x = \frac{1}{7}

Solution steps

x \cdot 3 + 2 x \cdot 2 + 5 s i x = 1

Rewrite

x 3 + 2 x 2 + 5 s i x

in standard complex form:

7 x + 5 x s i

7 x + 5 x s i = 1

Rewrite

1

in standard complex form:

1 + 0 i

7 x + 5 x s i = 1 + 0 i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[7 x = 1 5 x s = 0]

[7 x = 1 5 x s = 0] : s = 0, x = \frac{1}{7}

s = 0, x = \frac{1}{7}

y, s i x^{2} + 8 y = y^{2}

(x + y i)^{2} = 2 + 2 i 3

- 3 + y i = x + 6 i

40 - w^{2} - 2 w \cdot i = 0

x^{2} - x i - 1 = 0