Question

With full explanation from the internet like before 3x2-6x+5=0

Answer 1

Answer:

$\sf x=1+i\sqrt{\dfrac{2}{3}} \ \quad and \quad \:x=1-i\sqrt{\dfrac{2}{3}}$

Explanation:

Given Expression:

• 3x² - 6x + 5 = 0

Use the Quadratic Formula:

$\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ \ ax^2 + bx + c = 0$

insert coefficients

$\Longrightarrow \sf x = \dfrac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:3\cdot \:5}}{2\cdot \:3}$

$\Longrightarrow \sf x = \dfrac{\left6\right\pm \sqrt{-24} }{6}$

$\Longrightarrow \sf x = \dfrac{\left6\right\pm 2\sqrt{6}i}{6}$

$\Longrightarrow \sf x =1 \pm i\dfrac{\sqrt{6} }{3}$

$\Longrightarrow \sf x=1+i\sqrt{\dfrac{2}{3}}, \quad 1-i\sqrt{\dfrac{2}{3}}$

Answer 2

• 3x²-6x+5=0

Use quadratic formula

$\\ \rm\Rrightarrow x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\\ \rm\Rrightarrow x=\dfrac{6\pm \sqrt{36-60}}{6}$

$\\ \rm\Rrightarrow x=\dfrac{6\pm\sqrt{-24}}{6}$

$\\ \rm\Rrightarrow x=\dfrac{6\pm2\sqrt{6}i}{6}$

$\\ \rm\Rrightarrow x=1\pm \dfrac{sqrt{2}i}{\sqrt{3}}$

$\\ \rm\Rrightarrow x=1\pm\sqrt{\dfrac{2}{3}}i$