Question

If a=7-4√3,find the value of √α+1/√α

Answer 1

Consider, a = 7 – 4√3
= 7 – 2×2×√3
= 4 + 3 – 2×2× √3
= 22 + (√3)2 – 2×2× √3
a = (2 – √3)2
∴ √a = 2 – √3  

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