Question

The sum of a natural number and its reciprocal is 50÷7 .find the number

Answer 1

The natural number is 7

Step-by-step explanation:

Given:

The sum of a natural number and its reciprocal is 50/7

To find:

the number

Solution:

Let's assume the natural number is x

The reciprocal of the natural number x will be 1/x

According to the given,

x+1/x= 50/7

x²+1 = 50

  x         7

x²+1 (7)= 50x

7x²+7=50x

7x²-50x+7=0

Using the factorization method

7x²-49x-x+7=0

7x(x-7)-1(x-7)=0

(x-7) (7x-1) =0

∴ (x-7)=0 or (7x-1)=0

∴ x-7=0 or 7x-1=0

∴ x=7 or 7x=1

∴ x=7 or x=1/7

But x is a natural number

so, it won't be in fraction

Thus the natural number will be 7

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