Question

if X=7+4root3 so solved the x+1/x

Answer 1

x = 7+4√3
1/x = 1(-4√3) / 7+4√3-4√3
1/x= -4√3/7

x+1/x =( 7+4√3) + (-4√3/7)
=(49+28√3 -4√3) /7
=(24√3 +49 ) / 7
={24√3} /7 + 7

Answer 2

Hey! mate here is ur ans
$x = 7 + 4 \sqrt{3} \\ x + \frac{1}{x} = 7 + 4 \sqrt{3} + \frac{ 1}{7 + 4 \sqrt{3} } \\ = \frac{ {(7 + 4 \sqrt{3) }}^{2} + 1}{7 + 4 \sqrt{3} } \\ = \frac {49 + 48 + 56 \sqrt{3} + 1 }{7 + 4 \sqrt{3} } \\ = \frac{98 + 5 \sqrt{3} }{7 + 4 \sqrt{3} } \\ rationalise \: it \\ \frac{98 + 5 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \frac{98(7 - 4 \sqrt{3} ) + 5 \sqrt{3} (7 - 4 \sqrt{3} )}{ ( {7}^{2} - {4 \sqrt{3}) }^{2} } \\ \frac{686 - 392 \sqrt{3} + 35 \sqrt{3} - 60}{49 - 48} \\ = 686 - 60 - 357 \sqrt{3} \\ = 626 - 357 \sqrt{3}$
Hope it helps u
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