Question

$\sqrt{ {3x}^{2} } + 4x - 7 \sqrt{3} = 0$
to solve this quadriatic equation
by factorization complete the following activity​

Answer 1

GIVEN :–

• A quadratic equation √3x² + 4x - 7√3 = 0.

TO FIND :–

• Find x by using Factors method .

SOLUTION :–

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$\bf \implies \: \sqrt{3} {x}^{2} + 4x - 7 \sqrt{3} = 0$

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• Now Splitting Middle term –

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$\bf \implies \: \sqrt{3} {x}^{2} + 7x - 3x - 7 \sqrt{3} = 0$

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$\bf \implies \: x( \sqrt{3}x + 7)- \sqrt{3}( \sqrt{3} x - 7 ) = 0$

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$\bf \implies \: (x - \sqrt{3}) ( \sqrt{3}x + 7) = 0$

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(i)ㅤ

$\bf \implies \: x - \sqrt{3}= 0$

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$\bf \implies \large{ \boxed{ \bf x = \sqrt{3}}}$

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(ii)

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$\bf \implies \: \sqrt{3}x + 7 = 0$

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$\bf \implies \: \sqrt{3}x = - 7$

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$\bf \implies \: x = - \dfrac{7}{ \sqrt{3} }$

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$\bf \implies \: x = - \dfrac{7}{ \sqrt{3} } \times \dfrac{ \sqrt{3} }{ \sqrt{3} }$

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$\bf \implies \large { \boxed{\bf x = - \dfrac{7 \sqrt{3} }{3}}}$

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• Hence , x = √3 , x = (-7√3)/3 .

Answer 2

$\purple{\mathbb{ANSWER}}$

$\sf \sqrt3{x²} + 4x - 7\sqrt3 = 0$

${\implies}\sf \sqrt3x² - 3x + 7x - 7\sqrt3 = 0$

${\implies}\sf \sqrt3x(x - \sqrt3) + 7(x - 3\sqrt) = 0$

${\implies}\sf (\sqrt3x + 7)(x - \sqrt3) = 0$

${\therefore}~~\sf \red{x = \frac{-7}{\sqrt3}} ~~\: and ~~\:\red {x = \sqrt3}$