Question

If x=7+4√3, find the value of (x=1by√x)

Answer 1

I think you want
√x + 1/√x = ?

x = 7 + 4√3

1/x = 1/(7 + 4√3)

= (7 - 4√3)/(7 + 4√3)(7 - 4√3)

= (7 -4√3)/{7² -(4√3)²}

=( 7 - 4√3)/(49 - 48 )

= (7 - 4√3)

hence, 1/x = 7 - 4√3
so, x + 1/x = ( 7 + 4√3) + ( 7 -4√3) = 14

then, (√x + 1/√x)² -2 = x + 1/x
( √x + 1/√x)² -2= 14
(√x + 1/√x)²= 16
take square root both sides,
(√x +1/ √x) = 4

Answer 2

Hey mate !

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Given :


x = 7 + 4√3


To find :


√x + 1 / √x


Solution :


x = 7 + 4√3


⇒ x = 4 + 3 + 4√3


⇒ x = 2² + √3² + 2 × 2 × √3


⇒ x = ( 2 + √3)²


⇒ √x = 2 + √3


Now,


1 / √x = 1 / 2 + √3 × 2 - √3 / 2 - √3


⇒ 1 / √x = 2 - √3 / 2² - √3²


⇒ 1 / √x = 2 - √3 / 4 - 3


⇒ 1 / √x = 2 - √3


Again,


√x + 1 / √x = 2 + √3 + 2 - √3


⇒ √x + 1 / √x = 2 + 2


⇒ √x + 1 / √x = 4


Hence,


√x + 1 / √x = 4

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Thanks for the question!

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