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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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