Question

21. The sum of a number and its reciprocal is 17/4. Find the number
$14 {52}^{8}$
​

Answer 1

Answer:

4,1/4

Step-by-step explanation:

Given that,

The sum of a number and its reciprocal is 17/4.

To find the number.

Let the required number be x.

Therefore, it's reciprocal = 1/x

Now, according to question,

=> x + 1/x = 17/4

=> (x^2+1)/x = 17/4

On cross Multiplying, we will get,

=> 4(x^2+1) = 17x

=> 4x^2 + 4 = 17x

=> 4x^2 - 17x + 4 = 0

=> 4x^2 - 16x - x + 4 = 0

Taking out common terms, we get,

=> 4x(x-4) -1(x-4) = 0

=> (x-4)(4x-1) = 0

Therefore, we will get,

=> x-4 = 0

=> x = 4

And

=> 4x - 1 = 0

=> 4x = 1

=> x = 1/4

Hence, the required number is 4 and 1/4.

Answer 2

4 and 1/4
is the answer