Question

The sum of a fraction and 7 times its reciprocal is 11/2. What is the fraction?

Answer 1

Hi Friend !!!

Here is ur answer !!!!

let the fraction be x

it's reciprocal = 1/x

x+7(1/x) = 11/2

2(x²+7 )= 11x

2x² + 14 = 11x

2x²-11x + 14 = 0

2x²-4x-7x+14 = 0

2x(x-2) - 7(x-2) = 0

(2x-7)(x-2) = 0

x = 2 and 7/2


So the required fraction is 7/2


Hope it helps u : )

Answer 2

Let the fraction be x,

x + 7(1/x) = 11/2

x + 7/x = 11/2

2(x² + 7) = 11x

2x² + 14 - 11x = 0

2x² - 11x + 14 = 0

2x² - (7 + 4)x + 14 = 0

2x² -7x - 4x + 14 =0

x(2x - 7) - 2(2x - 7) = 0

(2x - 7)(x - 2) = 0

2x - 7 = 0 or x - 2 = 0

x = 7/2 or x= 2


Given that x is a fraction, so, x = 7/2


Required fraction is 7/2



I hope this will help you


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