Question

form a quadratic equation for the given example : The sum of natural number and its reciprocal is 121/25

No spamm​

Answer 1

Given that sum of a natural number and its reciprocal is 121/25.

i.e.

$x + \dfrac{1}{x} = \dfrac{121}{25} \\ \ \: \: \: \: \: (where \: x \: is \: natural \: number)$

The quadratic equation can be formed as:-)

$x + \dfrac{1}{x} = \dfrac{121}{25} \\ \\ \dfrac{ {x}^{2} + 1 }{x} = \dfrac{121}{25}$

Now do cross multiply gives

$25 {x}^{2} + 25 = 121x \\ \\ 25 {x}^{2} - 121x + 25 = 0$

Which is the simplest quadratic equation possible .

But on solving this equation we will not get any natural number as x .

So,

there will be no natural number

whose sum with its reciprocal will be equals to 121/25