Question

The sum of a number and its reciprocal is 25/2.what is the number?

Answer 1

Correct Question :

The sum of a number and its reciprocal is 5/2 , what is the number ?

Answer :

2 or 1/2

Solution :

Let the required number be x .

Then , its reciprocal will be 1/x .

Now ,

As pet the question , the sum of the number and its reciprocal is 5/2 .

Thus ,

=> x + 1/x = 5/2

=> (x² + 1)/x = 5/2

=> 2(x² + 1) = 5x

=> 2x² + 2 = 5x

=> 2x² - 5x + 2 = 0

=> 2x² - 4x - x + 2 = 0

=> 2x(x - 2) - (x - 2) = 0

=> (x - 2)(2x - 1) = 0

=> Either (x - 2) = 0 OR (2x - 1) = 0

• If x - 2 = 0 , then x = 2

• If 2x - 1 = 0 , then x = 1/2

Hence ,

Desired number may be 2 or 1/2 .

Answer 2

Given :

• The sum of a number and its reciprocal is 25/2.

To Find :

• what is the number?

Solution :

Let the number be x

Reciprocal = 1/x

Since we are given that sum of a number and its reciprocal is 25/12.

So,

$: \implies \sf \: \: \: \: \:x+\frac{1}{x}=\frac{25}{12} \\ \\ </p><p> : \implies \sf \: \: \: \: \:x+\frac{1}{x}=\frac{25}{12} \\ \\ </p><p> : \implies \sf \: \: \: \: \:x^2+1=\frac{25}{12}x \\ \\ </p><p></p><p> : \implies \sf \: \: \: \: \:12x^2+12-25x=0 \\ \\ \:$

$</p><p> : \implies \sf \: \: \: \: \: (3x-4)(4x-3)=0 \:$

$: \implies\sf \: \: \: \: x=\frac{4}{3},\frac{3}{4}$

Thus the numbers are $\sf\frac{4}{3},\frac{3}{4}$