Question

If x^2 +1/x2 =23 find the value of x-1/x

Answer 1

Answer:

√21

Step-by-step explanation:

(x - 1/x)² = x² + 1/x² - 2 = 23 -2 = 21

x - 1/x = √21.

Answer 2

Answer:

The value of x-1/x is √21.

Step-by-step explanation:

Given,

${x}^{2} + \frac{1}{ {x}^{2} } = 23$

We know,

${a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab$

So,

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

According to question,

${(x - \frac{1}{x}) }^{2} + 2 = 23 \\ {(x - \frac{1}{x} )}^{2} = 21 \\ x - \frac{1}{x} = \sqrt{21}$

This is a problem of Algebra.

Some important Algebra's formulas:

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ {(x + y)}^{3} = {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} + {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} \\ {x}^{3} + {y}^{3} = {(x + y)}^{3} - 3xy(x + y) \\ {x}^{3} - {y}^{3} = {(x - y)}^{3} + 3xy(x - y) \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ {x}^{2} + {y}^{2} = {(x - y)}^{2} + 2xy \\ {x}^{2} - {y}^{2} = {(x + y)}^{2} - 2xy \\ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )$

Two more important Algebra's problem:

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

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