Question

2.1
(x² - (√3+1)x+√3=0​

Answer 1

Step-by-step explanation:

${x }^{2} - ( \sqrt{3 } + 1)x + \sqrt{3} \\ = {x}^{2} - \sqrt{3} x - x + \sqrt{3} \\ = x(x - \sqrt{3} ) - 1(x- \sqrt{3} ) \\ = (x - \sqrt{3} )(x - 1) \\ \\ therefore \\ x = \sqrt{3} \: \: and \: \: \: 1$

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Answer 2

$\bold \red \star \: \underline{Solution:-}$

${x}^{2} - ( \sqrt{3} + 1)x + \sqrt{3} = 0. \\ \\ D = {b}^{2} - 4ac. \\ \\ \: \: \: \: \: = {( \sqrt{3 } + 1)}^{2} - 4(1)( \sqrt{3} ). \\ \\ \: \: \: \: = 3 + 1 + 2 \sqrt{3} - 4 \sqrt{3} . \\ \\ \: \: \: \: = 4 - 2 \sqrt{3} . \\ \\ \: \: \: \: = 2(2 - \sqrt{3} ).$

$\bold \red \star \: \underline{Answer:-}$

$\red{\longrightarrow \: 2(2 - \sqrt{3} )}$