reciprocal of the number

Question

the sum of a number and 81times its reciprocal is -18. What are the numbers?

Answer 1

Let the number be  x

Given that the sum of a number and 81 times its reciprocal is 81

∴ x + 81/x  = -81

=> x^2 + 81 = -18x     [ Multiplying by x on both sides ]

=> x^2 + 18x - 81 = 0

=> x^2 + 9x + 9x  - 81 = 0

=> x(x + 9) + 9(x + 9) = 0

=> (x + 9)(x + 9) = 0

=> x + 9 = 0

=> x = -9

Therefore the number is -9.