Question

The sum of a number and its reciprocal is 10 , find the number(s).

Answer 1

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The sum of a number and its reciprocal is 103, find the number(s). Hence, the number (s) are 3 and (1)/(3).

Answer 2

Answer:

Let the number be x

:. According to given statement

x+1x=103

⇒x2+1x=103

⇒3x2+3=10x

⇒3x2−10x+3=0

⇒3x2−(9+1)x+3=0

⇒3x2−9x−x+3=0

⇒3x(x−3)−1(x−3)=0

⇒(3x−1)(x−3)=0

when 3x−1=0, x=13

and when x-3=0, x=3

Hence, the number (s) are 3 and (1)/(3)