Question

3x² - 2root 6x +2 splitting the middle term ​

Answer 1

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

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

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

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

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

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

$\bold{other \: root}$

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

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

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

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Answer 2

Solution :

Equation :

• 3x² - 2√6x + 2

By Splitting the Middle Term :

›› 3x² - 2√6x + 2

›› 3x² - √6x - √6x + 2

›› 3x² -(√2 .√3)x - (√2 . √3)x + 2

›› √3x (√3x - √2) - √2 (√3x - √2)

›› (√3x - √2)(√3x - √2)

Roots of the given Equation are :

√3 x - √2 = 0

√3x = √2

• x = √2/√3

OR

√3 x - √2 = 0

√3x = √2

• x = √2/√3

Hence

• Roots of the given Equation are √2/√3.

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