Question

The sum of a no: and it's reciprocal is 1 1/2 . find the no:?​

Answer 1

Answer:

$\large\boxed{\sf{ \frac{11 \pm \sqrt{105} }{4} } }$

Step-by-step explanation:

It's being given that,

The sum of a number and it's reciprocal is 11/2.

To find the number.

Let the number be 'x'

Therefore, it's reciprocal will be 1/x.

Now, according to question, we have,

$= > x + \frac{1}{x} = \frac{11}{2} \\ \\ = > \frac{ {x}^{2} + 1}{x} = \frac{11}{2} \\ \\ = > 2( {x}^{2} + 1) = 11x \\ \\ = > 2 {x}^{2} + 2 = 11x \\ \\ = > 2 {x}^{2} - 11x + 2 = 0 \\ \\ = > x = \frac{ - ( - 11) \pm \sqrt{ {( - 11)}^{2} - (4 \times 2 \times 2)} }{2 \times 2} \\ \\ = > x = \frac{11 \pm \sqrt{121 - 16} }{4} \\ \\ = > x = \frac{11 \pm \sqrt{105} }{4}$

Hence, the numbers are $\bold{ \frac{11 \pm \sqrt{105} }{4} }$