Question

If a=7-4√3. find the value of
√a+1 √a

Answer 1

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Given : a = 7- 4√3, therefore, 1/a = 1/(7- 4√3) 

⇒1/a = 1* (7+ 4√3)/(7- 4√3)*(7+ 4√3) 

⇒ 1/a = (7+ 4√3)/(7² - 4² * 3)
 
⇒ 1/a = (7+ 4√3)/(49 - 48) 

⇒  1/a = (7+ 4√3) 

⇒ a + 1/a = 7- 4√3 + 7+ 4√3 

⇒  a + 1/a = 14 - - - - (i) 

Now, (√a + 1/√a )² = a + 1/a + 2* √a * 1/√a

=> (√a + 1/√a)² = x + 1/a + 2 

=> (√a + 1/√a)² = 14 + 2 

=> (√a + 1/√a ) = √16 - - {considering only positive value} 

=> √a + 1/√a

= 4 ⇔ (Ans)

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Answer 2

Question is
If a = 7-4√3, find the value of √a+ 1 divide√a
Then
Solution:

Consider, a = 7 – 4√3
= 7 – 2×2×√3
= 4 + 3 – 2×2× √3
= 2square2 + (√3)square2 – 2×2× √3
a = (2 – √3)square2
∴ √a = 2 – √3

1/√a =1/2-√3
Multiply both upper & lower side by 2+√3

=> 1/2-√3 × 2+√3 /2-√3

=> 2+√3 /4-3
= 2+√3

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

Hope it's helpful