Question

If x = 4 - root 5 find the value of (x + 1/x)whole square - (x - 1/x)whole square

Answer 1

Given that :-

x = 4 - root5

Therefore,
1/x = 1/4 - root5

Or,
1/x = 4+root 5/ 16 - 5

1/x = 4 + root 5 / 11


Now,

We have to find the value of :-


(x + 1/x )^2 - (x - 1/x)^2


We can see here the formula of

a^2 - b^2
So,
This can be re written as


(a + b )(a - b )



So,
Putting this value only in our question format


This becomes

(x + 1/x)^2 - (x - 1/x)^2 = (x+1/x + x -1/x) (x + 1/x -x + 1/x)


This then further becomes(after simplification ) :-


= ( 2x)(2.1/x)

= 2x* 2/x = 4


Also, it can be solved by putting the values.

But, this is the easiest process to get the direct answer.

Answer 2

Answer:

The final answer is 4.

Step-by-step explanation:

Given, we have an equation and we need to find final answer of the given equation by applying the value given.

$x = 4- \sqrt{5}$

We need to find the value of

$(x + 1/x)^2$ $- (x-1/x)^2$

We need to first open the bracket and simplify the equation before moving on further and substituting x values into it.

$(x^2 + 2*x*1/x + 1 /x^2)$$- (x^2 - 2*x*1/x + 1 /x^2)$

$(x^2 +2 + 1/x^2)$$- (x^2 -2 + 1/x^2)$

$x^2 + 2 - 1/x^2 -x^2 +2 - 1/x^2$$x^2 -x^2 +2+2+1/x^2-1/x^2$

$2+2 =4$

Hence we do not need to apply the value of x into as we can simplify the solution and get the answer very easily rather than applying the value of x into it.

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