Question

THE SUM OF A NUMBER AND ITS RECIPROCAL IS 53/14. FIND THE NUMBER

Answer 1

Step-by-step explanation:

Let that number be x. The reciprocal of the number is 1/x.

Therefore, x + 1/x = 53/14.

If you recall, if you have something like 2 + 1/2, for example, that is the same thing as 2 1/2, which is the same thing as 5/2.

In order to go from 2 1/2 to 5/2, all I did was multipy the denominator of the 1/2 fraction (which is 2), by the whole number (which, in this case, is also 2) and add the digit in the numerator of the fraction (which is 1) to give [(2 x 2 )+ 1)] = 5

In your problem, x + 1/x, similarly, would give you [(x * x) + 1] = (x^2 + 1)/x = 53/14

From here you cross multiply to get 14 (x^2 + 1) = 53 x

If you rearrange and bring everything to the right hand side, you get 14(x^2) - 57x + 14 = 0.

You can then solve for x. (which is 2/7, by the way).

Answer 2

$\mathfrak{\huge{\underline{\underline{AnswEr :}}}}$

⚘ x + 1/x - 53/14 = 0

» multiply by 14x get

⚘ 14x² - 53x + 14 = 0

⚘ (2x-7)(7x-2) = 0

So x = 7/2 or x = 2/7