Question

Solve this by completing square method=find its roots
root3x²+10x+7root3​

Answer 1

Step-by-step explanation:

Solve by this by completing square method

$\sqrt{3} {x}^{2} + 10x + 7 \sqrt{3} = 0 \\ \\ divide \: eq \: by \: \sqrt{3} \\ \\ {x}^{2} + \frac{10}{ \sqrt{3} }x + 7 = 0\\ \\ take \: 7 \: to \: other \: side \\ \\ {x}^{2} + \frac{10}{ \sqrt{3} }x = - 7 \\ \\ {(x)}^{2} + 2(x)( \frac{5}{ \sqrt{3} } ) + {( \frac{5}{ \sqrt{3} } )}^{2} = - 7 + {( \frac{5}{ \sqrt{3} }) }^{2} \\ \\ ( {x + \frac{5}{ \sqrt{3} }) }^{2} = - 7 + \frac{25}{3} \\ \\ ( {x + \frac{5}{ \sqrt{3} }) }^{2} = \frac{ - 21 + 25}{3} \\ \\ ( {x + \frac{5}{ \sqrt{3} }) }^{2} = \frac{4}{3} \\ \\ ( {x + \frac{5}{ \sqrt{3} }) }^{2} = ( { \frac{2}{ \sqrt{3} }) }^{2} \\ \\ ( {x + \frac{5}{ \sqrt{3} }) }^{2} - ( { \frac{2}{ \sqrt{3} }) }^{2} = 0 \\ \\ \because \: {a}^{2} - {b}^{2} = (a + b)(a - b)\\ \\ (x + \frac{5}{ \sqrt{3} } + \frac{2}{ \sqrt{3} } )(x + \frac{5}{ \sqrt{3} } - \frac{2}{ \sqrt{3} } ) = 0 \\ \\ (x + \frac{7}{ \sqrt{3} } )(x + \frac{3}{ \sqrt{3} } ) = 0 \\ \\ roots \: are \\ \\ x = - \frac{7}{ \sqrt{3} }\:or\:x= -\frac{7\sqrt{3} }{3}\: \\ \\ and \\ \\ x = \frac{ - 3}{ \sqrt{3} }\:or\:x= -\sqrt{3}$

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