9. Simplify by rationalising the denominator: 2+√3 2−√3 + 2−√3 2+√3 .

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9. Simplify by rationalising the denominator: 2+√3 2−√3 + 2−√3 2+√3 .

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Thu Hương 1 year 2021-09-01T12:03:01+00:00 1 Answers 2 views 0

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  1. dangkhoa
    0
    2021-09-01T12:04:14+00:00
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    [tex]\implies {\blue {\boxed {\boxed {\purple {\sf { 14 }}}}}}[/tex]

    [tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

    [tex] \frac{2 + \sqrt{3} }{2 – \sqrt{3} } + \frac{2 – \sqrt{3} }{2 + \sqrt{3} } [/tex]

    [tex] \\= \frac{2 + \sqrt{3} }{2 – \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } + \frac{2 – \sqrt{3} }{2 + \sqrt{3} } \times \frac{2 – \sqrt{3} }{2 – \sqrt{3} } [/tex]

    [tex] \\= \frac{2 \: (2 + \sqrt{3} )+ \sqrt{3} \: (2 + \sqrt{3} )}{ ({2})^{2} – ({ \sqrt{3} })^{2} } + \frac{2 \: (2 – \sqrt{3} ) – \sqrt{3} \: (2 – \sqrt{3} ) }{ ({2})^{2} – ( { \sqrt{3} })^{2} } [/tex]

    [tex]\\ = \frac{4 + 2 \sqrt{3} + 2 \sqrt{3} + 3 }{4 – 3} + \frac{4 – 2 \sqrt{3} – 2 \sqrt{3} + 3}{4 – 3} [/tex]

    [tex]\\ = \frac{7 + 4 \sqrt{3} }{1} + \frac{7 – 4 \sqrt{3} }{1} [/tex]

    [tex] \\= 7 + 4 \sqrt{3} + (7 – 4 \sqrt{3} )[/tex]

    [tex] \\= 7 + 4 \sqrt{3} + 7 -4 \sqrt{3} [/tex]

    [tex] \\= 14[/tex]

    Note:

    [tex] (a + b)(a – b) = {a}^{2} – {b}^{2} [/tex]

    [tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]

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