Question

If = 7 − 4√3, find the value of √a + 1 /√a .

I need it quickly and step by step, please

Answer 1

Step-by-step explanation:

i think this is the answer

Answer 2

Step-by-step explanation:

a= 7-4√3

1/a = 1/(7-4√3)

on rationalising

1/a = {1×(7+4√3)}/{(7-4√3)(7+4√3)

1/a = (7+4√3)/49-48.

{using (a+b)(a-b) = a^2 -b^2 }

1/a = 7+4√3

now

a + 1/a = 7-4√3 + 7 + 4√3

a+ 1/a = 14

we can write (a) = (√a)^2

because of √a×√a= a

(√a)^2 + (1)^2/ (√a)^2 = 14

(√a)^2 + {1/(√a)}^2 = 14

add 2(√a)(1/√a) both sides

(√a)^2 +{1/(√a)}^2 + 2(√a)(1/√a) = 14 + 2(√a)(1/√a)

using (a)^2 + (b)^2 + 2 ab = (a+ b ) ^2

( √a + 1/√a)^2 = 14 + 2 { 2√a × 1/√a =2}

(√a +1/√a ) = √16

√a+1/√a = 4 or -4