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Solve for x: √(3x^2)−2√2-2√3=0 - Mathematics

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Solve for x: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`

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Solution

`sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`

Hencea`Hence a=sqrt3, b=-2sqrt2,c=-2sqrt3`

`x=(-(-2sqrt2)+-sqrt((-2sqrt2)^2-4xxsqrt3xx(-2sqrt3)))/(2xxsqrt3)`

`=(2sqrt2+-sqrt(8+24))/(2sqrt3)`

`=(2sqrt2+-sqrt32)/(2sqrt3)`

`=(2sqrt2+-4sqrt2)/(2sqrt3)`

`=(2sqrt2+4sqrt2)/(2sqrt3),(2sqrt2-4sqrt2)/(2sqrt3)`

`=(3sqrt2)/(2sqrt3),(-2sqrt2)/(2sqrt3)`

`x=sqrt6,-sqrt(2/3)`

Concept: Nature of Roots
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