Question

The sum of a number and its reciprocal is 122 / 11. Find the number.

Answer 1

Hi friend, Harish here.

Here is your answer:

Given that,

Sum of a number and it's reciprocal is 122 by 11.

To find, 

The number .

Solution,

Let the number be ' x '.

Then,

$x+ \frac{1}{x} = \frac{122}{11}$

→ $\frac{x^{2} +1}{x} = \frac{122}{11}$

Now, Cross multiply 11 & x.

→ $11x^{2}+11 = 122x$

→ $11x^{2} -122x + 11 = 0$

→ $11x^{2}-121x - 1x +11=0$

→ $11x(x-11)-1(x-11)=0$

→ $(11x-1) (x-11) =0$

If the above equation must be zero,

Then,

→ $11x-1 =0$

→ $11x=1$

→ $x= \frac{1}{11}$

Or,

→ $x-11=0$

→ $x=11$

Therefore the value of the number & it's reciprocal is 11 & 1/11.
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Hope my answer is helpful to you.