Question

x=7+4√3, find (x+ 1divide by √x)

Answer 1

$x = 7 + 4 \sqrt{3} \: \: - (1) \\ \frac{1}{x} = \frac{1}{7 + 4 \sqrt{3} } = \frac{7 - 4 \sqrt{3} }{ {7}^{2} - {(4 \sqrt{3}) }^{2} } \\ \frac{1}{x} = \frac{7 - 4 \sqrt{3} }{49 - 48} = 7 - 4 \sqrt{3} \: \: - (2) \\ \\ (1) + (2) = x + \frac{1}{x} \\ = 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3} = 14$
please follow me

Answer 2

Consider, a = 7 – 4√3
= 7 – 2×2×√3
= 4 + 3 – 2×2× √3
= 2

2

+ (√3)

2

– 2×2× √3
a = (2 – √3)

2

∴ √a = 2 – √3
Hence [(√a)+ (1/√a)] = 2 – √3 +2 + √3 
 = 4