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Marina CMI [18]
2 years ago
11

Find the roots of the equation x^2 +7= 2x express your answer in simplest a +bi form

Mathematics
1 answer:
Fittoniya [83]2 years ago
7 0

x^2+7=2x\\\\\implies x^2 -2x +7 =0\\\\\text{Apply quadratic formula,}~ x =\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{in this case,}~ a = 1, b= -2 ~\text{and}~ c = 7\\\\\\x= \dfrac{-(-2) \pm \sqrt{(-2)^2 -4\cdot 1 \cdot 7}}{2\cdot 1}\\\\\\\implies x =\dfrac{2 \pm \sqrt{-24}}{2}\\\\\\\implies x = \dfrac{2 \pm i\sqrt{24}}2\\\\\implies x =\dfrac{2 \pm i2\sqrt{6}}2\\\\\implies x = \dfrac{2\left(1 \pm i  \sqrt 6\right)}2\\\\\implies x = 1 \pm i\sqrt 6\\\\

\text{Hence,}~ x = 1-i\sqrt 6 ~\text{or}~ x = 1+i\sqrt 6

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Answer: \Large\boxed{f(x-1)=x}

Step-by-step explanation:

<u>Given function</u>

f(x + 1) = x + 2

<u>Isolate [ x + 1 ] on the right-hand side</u>

f(x + 1) = x + 1 + 1

f(x + 1) = (x + 1) + 1

<u />

<u>Substitute [ x + 1 ] with x</u>

f(x) = x + 1

<u>Substitute [ x ] with [ x - 1 ]</u>

f(x - 1) = (x - 1) + 1

\Large\boxed{f(x-1)=x}

Hope this helps!! :)

Please let me know if you have any questions

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