Question

the sum of a number and it's reciprocal is 5/2 .Find the number​

Answer 1

Step-by-step explanation:

reciprocal of 5/2=2/5

5/2+2/5

lcm of 2 and 5 is 10.

25/10+4/10=25+4/10

=29/10

=2.9

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Answer 2

Answer:

The numbers are 2 and 1/2

Step-by-step explanation:

Given :

The sum of a number and it's reciprocal = 5/2

To find : Numbers

Let the 1st number be x and the other be 1/x

According to Question

$x + \frac{1}{x} = \frac{5}{2}$

Now take the L.C.M

$\frac{ {x}^{2} + 1 }{x} = \frac{5}{2} \\ \\ 2( {x}^{2} + 1) = 5x \\ \\ 2 {x}^{2} + 2 = 5x \\ \\ 2 {x}^{2} - 5x + 2 = 0$

Here , we get an quadratic equation in x

Apply middle term splitting

$2 {x}^{2} - 5x + 2 = 0 \\ \\ 2 {x}^{2} - 4x - x + 2 = 0 \\ \\ 2x(x - 2) - 1(x - 2) = 0 \\ \\ (2x - 1) \times (x - 2) = 0$

Now, equate the factors to get Zero

$2x - 1 = 0 \\ \\ 2x = 1 \\ \\ x = \frac{1}{2}$

Equate the other factor to zero

$x - 2 = 0 \\ \\ x = 2$

So, We get $\boxed{\bold{\mathsf{X = 2 \: and \: x =\frac{1}{2}}}}$

The numbers are 2 and 1/2