The difference between a positive fraction and its reciprocal is 9 20 9 20 . Find the sum of that fraction and its reciprocal. Options : 41/20 17/20 none 9/20

Let's denote the fraction as x. Its reciprocal would then be 1/x.

According to the problem, the difference between the fraction and its reciprocal is 9/20. This can be written as:

x - 1/x = 9/20

To solve this equation, we can multiply every term by 20x to get rid of the fraction:

20x^2 - 20 = 9x

Rearranging the terms gives us a quadratic equation:

20x^2 - 9x - 20 = 0

We can solve this quadratic equation using the quadratic formula:

x = [9 ± sqrt((9)^2 - 420(-20))]/(2*20) x = [9 ± sqrt(81 + 1600)]/40 x = [9 ± sqrt(1681)]/40 x = [9 ± 41]/40

This gives us two possible solutions for x: x = 50/40 = 5/4 or x = -32/40 = -4/5.

However, since we're looking for a positive fraction, we discard the negative solution. So, x = 5/4.

The sum of the fraction and its reciprocal is then:

x + 1/x = 5/4 + 4/5 = 25/20 + 16/20 = 41/20

So, the correct answer is 41/20.

Let's denote the fraction as x. Its reciprocal would be 1/x.

According to the problem, we have the equation:

x - 1/x = 9/20

To solve this equation, we can multiply every term by 20x to get rid of the fractions:

20x^2 - 20 = 9x

Rearrange the equation to form a quadratic equation:

20x^2 - 9x - 20 = 0

Divide every term by 20 to simplify:

x^2 - 9/20*x - 1 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve it using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a):

x = [9/20 ± sqrt((9/20)^2 - 4*(-1))] / 2 x = [9/20 ± sqrt(81/400 + 4)] / 2 x = [9/20 ± sqrt(1681/400)] / 2 x = [9/20 ± 41/20] / 2

We have two solutions: x = 50/20 = 5/2 and x = -32/20 = -8/5.

However, since x is a positive fraction, we discard the negative solution. So, x = 5/2.

The sum of the fraction and its reciprocal is then x + 1/x = 5/2 + 2/5 = 25/10 + 4/10 = 29/10 = 2.9.

So, the answer is none of the given options.