Question

3x^2ー2 root6x + 2 = 0​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

${ \large \bold\green { \mathbb{ \underline{GIVEN}} \hookrightarrow}}</p><p>$

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

${ \large \bold\green { \mathbb{ \underline{TO \: \: FIND}} \hookrightarrow}}</p><p>$

$\sf \: values \: of \: x$

${ \large \bold\green { \mathbb{ \underline{SOLUTION}} \hookrightarrow}}</p><p>$

$\sf \: {3x}^{2} - 2 \sqrt{6} x + 2 = 0 \\ \sf \green\implies \: 3 {x}^{2} - \sqrt{6} x - \sqrt{6} x + 2 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \green\implies \: \sqrt{3} x( \sqrt{3} x - \sqrt{2} ) - \sqrt{2} ( \sqrt{3} x - \sqrt{2} ) \: = 0 \\ \sf \green\implies \: (\sqrt{3} x - \sqrt{2} )( \sqrt{3} x - \sqrt{2} ) = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf \: \sqrt{3} x - \sqrt{2} = 0 \\ \sf \green\implies \sqrt{3} x = \sqrt{2} \: \: \\ \sf \green\implies \: x = \frac{ \sqrt{2} }{ \sqrt{3} } \: \: \: \: \: \\ \sf \green\implies \: x = \sqrt{ \frac{2}{3} }$

$\green{ \boxed{ \sf \: hence \: \: x = \sqrt{ \frac{2}{3} }}}$