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Class-9»Maths

if a = 7-4 root 3 then find the value of root a +1/ root a

$G i v e n, a = 7 - 4 \sqrt{3} \frac{1}{a} = \frac{1}{7 - 4 \sqrt{3}} \times \frac{7 + 4 \sqrt{3}}{7 + 4 \sqrt{3}} \Rightarrow \frac{1}{a} = \frac{7 + 4 \sqrt{3}}{49 - 48} \Rightarrow \frac{1}{a} = 7 + 4 \sqrt{3} T h u s, a + \frac{1}{a} = (7 - 4 \sqrt{3}) + (7 + 4 \sqrt{3}) = 14 W e k n o w t h a t, {(\sqrt{a} + \frac{1}{\sqrt{a}})}^{2} = a + \frac{1}{a} + 2 \Rightarrow {(\sqrt{a} + \frac{1}{\sqrt{a}})}^{2} = 14 + 2 = 16 \Rightarrow (\sqrt{a} + \frac{1}{\sqrt{a}}) = \sqrt{16} = 4 \Rightarrow \sqrt{a} + \frac{1}{\sqrt{a}} = 4$

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