Question

If a number is added to its reciprocal, the result is 5/2. Find the numbers

Answer 1

According to the question
Let the number be x

`x+(1)/(x)=(5)/(2) \\\\\ (x^(2)+1)/(x) = (5)/(2) \\\\\\\ By \\ cross-multiplication \\\\x^(2)+1 = (5)/(2) * x\\\\2x^(2)+2 = 5x\\\\2x^(2)-5x+2 = 0\\\2x^2-4x-1x+2 = 0\\2x(x-2)-(x-2)=0\\(2x-1)(x-2)=0\\\\therefore,\\\\x = (1)/(2)\\or\\x = 2`