Question

quadratic equation by factorization method

3x²-2√6x+2=0

Answer 1

"3x2 – 2 √6 +2=0

We will factorize splitting the middle term method 3x2 – √6 −√6 +2=0

3x2 – √(2×3) −√(2×3) +2=0

3x2 – (√2)(√3)−(√2)(√3)+2=0

√3 (√3 −√2 )−√2 (√3 −√2 )=0

(√3 −√2) (√3 −√2)=0

Hence x =√(2/3) & x =√(2/3) are roots of the equation

The answer will be √2 / √3

Or

3x² - 2√6x + 2 = 0

a = 3 ; b = -2√6 ; c = 2

We have

▲ = b² - 4ac = (-2√6)² - 4.3.2 = 24-24 = 0

=> Only one x

=> x = -b / 2a = 2√6 / 3.2 = √6 / 3

"

Answer 2

Hello Brother

Topic:- Quardratic Equation

Equation:-

$\bold{ {3x}^{2} - 2 \sqrt{6x} + 2 = 0}$

$\bold{ \sqrt{3x} ( \sqrt{3x} - \sqrt{2} ) - \sqrt{2} ( \sqrt{3x} - \sqrt{2} ) = 0}$

$\bold{( \sqrt{3x} - \sqrt{2} )( \sqrt{3x} - \sqrt{2}) = 0}$

$\bold{ \sqrt{3x} = \sqrt{2} }$

$\bold{ \sqrt{3x} =- \sqrt{2}}$

$\bold{x = \frac{ \sqrt{2} }{ \sqrt{3} }}$

$\bold{other \: root}$

$\bold{ \sqrt{3x} - \sqrt{2} = 0}$

$\bold{ \sqrt{3x} =- \sqrt{2}}$

$\bold{x = \frac{ \sqrt{2} }{ \sqrt{3} }}$

Thanks!!!