Question

if $a=7-4\sqrt{x} , \\value?= \sqrt{a} +1/\sqrt{a}$

please answer this ASAP
and please the correct answer

Answer 1

Answer:

√a + 1/√a = 4

Solution:

• Given : a = 7 - 4√3
• To find : √a + 1/√a

We have ;

=> a = 7 - 4√3

=> a = 4 + 3 - 4√3

=> a = 4 - 4√3 + 3

=> a = 2² - 2×2×√3 + (√3)²

=> a = (2 - √3)²

=> √a = 2 - √3

Thus,

=> 1/√a = 1/(2 - √3)

=> 1/√a = (2 + √3)/(2 - √3)(2 + √3)

=> 1/√a = (2 + √3)/[ 2² - (√3)² ]

=> 1/√a = (2 + √3)/(4 - 3)

=> 1/√a = (2 + √3)/1

=> 1/√a = 2 + √3

Now,

=> √a + 1/√a = 2 - √3 + 2 + √3

=> √a + 1/√a = 4

Hence,

√a + 1/√a = 4