Question

If x^2+1/x^2=146 then find the value of x-1/x

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The answer is 12.

Given: $x^{2} + \frac{1}{x^{2} }$ = 146

To Find: the value of $x-\frac{1}{x}$

Solution:

We know the algebraic identity,

$(x-\frac{1}{x})^{2}$ = $x^{2} + \frac{1}{x^{2} }$ -2

Substituting the values, we get,

$(x-\frac{1}{x})^{2}$ = 146 - 2

             = 144

⇒ $(x-\frac{1}{x})$ = $\sqrt{144}$

               = 12

Answer) The required value is 12.

Note

• This sum has been given in the chapter on Algebraic Expressions. Algebraic expressions refer to the generalized formula which is created by using different alphabetical variables and can be used in various sums.

• In the given sum, we needed to use an algebraic identity. It is a simple identity $(x-\frac{1}{x})^{2}$. We needed to use the expansion of this algebraic expression to solve this sum.

• We can input the values of these variables into the expression to find out the values of the variables x and y. Since the value of a part of the expression is given in the sum, we can easily find out the value  $(x-\frac{1}{x})$ from the expression.

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