Question

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

Answer 1

• 3x²-6x+5=0

Use quadratic formula

`\\ \rm\Rrightarrow x=(-b\pm√(b^2-4ac))/(2a)`

`\\ \rm\Rrightarrow x=(6\pm √(36-60))/(6)`

`\\ \rm\Rrightarrow x=(6\pm√(-24))/(6)`

`\\ \rm\Rrightarrow x=(6\pm2√(6)i)/(6)`

`\\ \rm\Rrightarrow x=1\pm \frac{sqrt{2}i}{√(3)}`

`\\ \rm\Rrightarrow x=1\pm\sqrt{(2)/(3)}i`

Answer 2

`\sf x=1+i\sqrt{(2)/(3)} \ \quad and \quad \:x=1-i\sqrt{(2)/(3)}`

Step-by-step explanation:

Given Expression:

• 3x² - 6x + 5 = 0

Use the Quadratic Formula:

`\sf x = ( -b \pm √(b^2 - 4ac))/(2a) \ \ when \ \ ax^2 + bx + c = 0`

insert coefficients

`\Longrightarrow \sf x = (-\left(-6\right)\pm √(\left(-6\right)^2-4\cdot \:3\cdot \:5))/(2\cdot \:3)`

`\Longrightarrow \sf x = (\left6\right\pm √(-24) )/(6)`

`\Longrightarrow \sf x = (\left6\right\pm 2√(6)i)/(6)`

`\Longrightarrow \sf x =1 \pm i(√(6) )/(3)`

`\Longrightarrow \sf x=1+i\sqrt{(2)/(3)}, \quad 1-i\sqrt{(2)/(3)}`