Question

Find Root. (1) 3x² -5x +3 =0​

Answer 1

ANSWER:

$3 {x}^{2} - 5x + 3 = 0$

$using \: completing \: square \: method$

$3 {x}^{2} - 5x + 3 = 0$

$3 {x}^{2} - 5x = - 3$

$dividing \: by \: 3 \: on \: both \: sides$

$\frac{3 {x}^{2} }{3} - \frac{5x}{3} = \frac{ - 3}{3}$

${x}^{2} - \frac{5x}{3} = - 1$

$({x})^{2} - 2(x)( \frac{5}{6}) = - 1$

$adding \: ({ \frac{5}{6} })^{2} \: on \: both \: sides$

${(x)}^{2} - 2(x)( \frac{5}{6}) + (\frac{5}{6} )^{2} = - 1 + ( \frac{5}{6})^{2}$

$using \: formula \: {( a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

${(x - \frac{5}{6}) }^{2} = - 1 + \frac{25}{36}$

${(x - \frac{5}{6}) }^{2} = \frac{ - 36}{36} + \frac{25}{36}$

$( { x - \frac{5}{6} })^{2} = \frac{ - 36 + 25}{36}$

$( {x - \frac{5}{6}) }^{2} = \frac{11}{36}$

$taking \: square \: root \: on \: both \: sides$

$\sqrt{( {x} - \frac{5}{6})^{2} } = \sqrt{ \frac{11}{36} }$

$x - \frac{5}{6} = \frac{ + }{} \frac{ \sqrt{11} }{ \sqrt{36} }$

$x - \frac{5}{6} = \frac{ + }{} \frac{ \sqrt{11} }{6}$

$x = \frac{5}{6} \frac{ + }{} \frac{ \sqrt{11} }{6}$

$x = \frac{5 \frac{ + }{} \sqrt{11} }{6}$

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