Question

solve this question ,algebra

Answer 1

In the attachments I have answered this problem.

Make use of this identity

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

the value of the required expression is found.

See the attachments for detailed solution.

Answer 2

HELLO DEAR,

given, x = 2 + √3 . AND 2x = 2(2 + √3)

$\bold{1/x = 1/(2 + \sqrt{3}) * (2 - \sqrt{3})/(2 - \sqrt{3})}$

$\bold{1/x = (2 - \sqrt{3})/(4 - 3)}$

$\bold{1/x = (2 - \sqrt{3}) \:\:AND\:\:1/2x = (2 - \sqrt{3})/2}$

Now, we have to find (√2x + 1/√2x)=?

now, on squaring of (√2x + 1/√2x)²

(√2x + 1/√2x)² = (2x + 1/2x + 2*√2x * 1/√2x)

now put the values of 2x , 1/2x

(√2x + 1/√2x)² = [2(2 + √3) + (2 - √3)/2 + 2]

(√2x + 1/√2x)² = [(8 + 4√3 + 2 - √3)/2 + 2]

(√2x + 1/√2x)² = (10 + 3√3+4)2

(√2x + 1/√2x) = $\bold{\sqrt{(14+ 3\sqrt{3})/2}}$

(√2x + 1/√2x) = $\bold{\sqrt{7 + 3\sqrt{3}/2}}$

I HOPE ITS HELP YOU DEAR,
THANKS