Question

if a=7-4√3 prove that √a+1/√a=4

Answer 1

Hello twinkle!
#ur Ans
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Given that

$a = 7 - 4 \sqrt{3} \\ \\ \frac{1}{a} = \frac{1}{7 - 4 \sqrt{3} } \\ \\ now \: rationlisng \\ \\ \frac{1}{a} = \frac{1}{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ \frac{1}{a} = \frac{7 + 4 \sqrt{3} }{ {7}^{2} - (4 \sqrt{3} {)}^{2} } \\ \\ \frac{1}{a} = \frac{7 + 4 \sqrt{3} }{49 - 48} \\ \\ \frac{1}{a} = 7 + 4 \sqrt{3} \\ \\ now \\ \\ ( \sqrt{a} + \frac{1}{ \sqrt{a} } {)}^{2} = a + \frac{1}{a} + 2 \\ \\ put \: the \: value \\ \\ ( \sqrt{a} + \frac{1}{ \sqrt{a} } {)}^{2} = 7 - 4 \sqrt{3} + 7 + 4 \sqrt{3} + 2 \\ \\ ( \sqrt{a} + \frac{1}{ \sqrt{a} } {)}^{2} = 16 \\ \\ ( \sqrt{a} + \frac{1}{ \sqrt{a} } ) = \sqrt{16} \\ \\ ( \sqrt{a} + \frac{1}{ \sqrt{a} } ) = 4 \\ \\ hence \: proved$

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