Question

if x+1/x = 6 find x -1/x

Answer 1

Answer:

hey here is your correct answer

Step-by-step explanation:

x+1/x=6

x+1=6x

1=5x

1/5=x

replace value of x in the second equation

1/5-1/1/5

5 goes up therefore

1/5-5/1

LCM=5

1/5-5x5/1x5

1-25/5

=    -24/5

Answer 2

Given,

x + (1/x) = 6

To find,

The value of (x - 1/x).

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the value of (x - 1/x) is equal to p.

Mathematically,

If a and b are two variables, then there exists an algebraic expression such that,(a) (a+b)^2 = a^2 + b^2 + 2ab

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

{Statement-1}

According to the question,

On squaring both the sides of the given equation, we get;

(x + 1/x)^2 = (6)^2

=> x^2 + 1/x^2 + 2(x)(1/x) = 36

{According to statement-1 (a)}

=> x^2 + 1/x^2 + 2 = 36

=> x^2 + 1/x^2 = 36 - 2

=> x^2 + 1/x^2 = 34 ------------{Equation-1}

Now, as assumed,

(x - 1/x) = (p)

On squaring both the sides of the equation, we get;

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

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

{according to statement-1 (b)}

=> x^2 + 1/x^2 - 2 = p^2

=> p^2 = 34 - 2 = 32

{according to equation-1}

=> p = √32

=> (x - 1/x) = 4√2

Hence, the value of (x - 1/x) is equal to 4√2.