If x = 2-Sqrt(3) then find the Value of x^2+1/x^2 = ?? Please Explain?

Answer 1

x^2+1/x^2=(x+1/x)^2-2
x=2-rt3
1/x=1/2-rt3
rationalising the Dr 1/x=2+rt3/(2-rt3)(2+rt3)
=2+rt3/4-1
=2+rt3
so (x+1/x)^2-2
=(2-rt3+2+rt3)^2-2
=16-2
=14

Answer 2

x = 2 - √3

First work out the value of x^2.
x^2 = (2 - √3)^2 = 4 - 4√3 + 3 = 7 - 4√3.

Therefore, 1 / x^2 = 1 / (7 - 4√3)

To get rid of the radical in the denominator,
you have to multiply both numerator and
denominator by 7 + 4√3, which, in effect,
is just multiplying by 1, which doesn't change
the value of the expression, but does make the
denominator easier to deal with.

So, 1 / x^2 = 1 / (7 - 4√3)

= 1 * (7 + 4√3) / [(7 - 4√3)(7 + 4√3)]

= (7 + 4√3) / (49 - 4^2 * 3)

= 7 + 4√3

So now we have,

(x^2) + (1 / x^2) = (7 - 4√3) + (7 + 4√3) = 14

Answer 3

x = 2 - sqrt(3)

And we want to find the value of

(x^2 + 1)/x^2

So we start by plugging in the value and seeing what we get.

[ {2 - sqrt(3)}^2 + 1] / [2 - sqrt(3)]^2

We start by first expanding. (2 - sqrt(3)) occurs twice in the equation, so we can actually solve for it separately here and then replace.

(2 - sqrt(3))^2 = 4 - 4sqrt(3) + 3 = [7 - 4sqrt(3)]. Replacing, we get

[7 - 4sqrt(3) + 1] / [7 - 4sqrt(3)]

Grouping like terms, we get

[8 - 4sqrt(3)] / [7 - 4sqrt(3)]

It is proper mathematical etiquette to NOT have a radical (or square root) symbol in the denominator of any fraction. For that reason, we have to eliminate it, by multiplying the denominator by the conjugate. The conjugate of (a + b) is (a - b), and the result of multiplying something by its conjugate leads to a difference of squares. Remember that a^2 - b^2 factors into (a-b)(a+b), and we're essentially going in the opposite direction.

In our case, the conjugate we want to multiply top and bottom by is [ 7 + sqrt(3) ]

[8 - 4sqrt(3)] [7 + sqrt(3)] / [7 - 4sqrt(3)] [7 + 4sqrt(3)]

Resulting in

[56 + 8sqrt(3) - 28sqrt(3) - 4(3)] / [49 - 16(3)]
[56 - 20sqrt(3) - 12] / [49 - 48]
[44 - 20sqrt(3)]/(1)

So your final answer is

44 - 20sqrt(3)

Answer 4

hI, it is simple,
u just substitute the value of x in the eqaution to solve as follows:
(2-Sqrt(3))^2 + 1/(2-Sqrt(3))^2
which equals
(((2-Sqrt(3))^4)+1)/(2-Sqrt(3))^2
which on solving gives:
(98-56*sqrt(3))/(2-Sqrt(3))^2

Answer 5

just substitute the value of x to your equation and perform the indicated operation and your problem is finished

since your x=2-sqrt3 and your equation is x^2+1/x^2
try first to solve the value of x^2 =(2-sqrt3)^2
x^2=7-sqrt3 if i solved it properly hehehe
use this valeu to your equation
(7-sqrt3)+1/(7-sqrt3)
then simplify

(53-14sqrt3)/(7-sqrt3) if im not mistaken this is your final answer