Question

Please solve this equation... ​

Answer 1

Answer:

x = 3, ⅓

Step-by-step explanation:

Given an equation such that,

$x + \frac{1}{x} = 3 \frac{1}{3}$

Where, x≠0

To solve this.

Taking LCM of denominators and solving, we get,

$= > \frac{ {x}^{2} + 1}{x} = \frac{3 \times 3 + 1}{3} \\ \\ = > \frac{ {x}^{2} + 1}{x} = \frac{9 + 1}{3} \\ \\ = > \frac{ {x}^{2} + 1 }{x} = \frac{10}{3}$

On cross multiplying, we will get,

$= > 3( {x}^{2} + 1) = 10x \\ \\ = > 3 {x}^{2} + 3 = 10x \\ \\ = > 3 {x}^{2} - 10x + 3 = 0$

So, we have a quadratic equation.

To solve this, we will use middle term splitting method.

Therefore, we will get,

$= > 3 {x}^{2} - 9x - x + 3 = 0$

Taking out common terms, we get,

$= > 3x(x - 3) - 1(x - 3) = 0 \\ \\ = > (x - 3)(3x - 1) = 0$

Therefore, we have,

=> x - 3 = 0

=> x = 3

And,

=> 3x - 1 = 0

=> x = ⅓

Hence, the required solutions are 3 and ⅓.

Answer 2

Solution:

=> x + 1/x = 3 ⅓

=> x² + 1/x = 10/3

By cross multiplication

=> 10x = 3(x² + 1)

=> 10x = 3x² + 3

=> 3x² + 3 - 10x = 0

It can be written as

=> 3x² - 10x + 3 = 0

Now , we have got a quadratic equation findind x by factorisation

First , splitting the middle term

=> 3x² - 9x - x + 3 = 0

Taking common

=> 3x(x - 3) - 1(x - 3) = 0

=> (x - 3)(3x - 1) = 0

Now , either x - 3 = 0 or 3x - 1 = 0

♦ x - 3 = 0

♦ x = 3

→ 3x - 1 = 0

→ 3x = 1

→ x = ⅓

Hence , x = 3 or 1/3