Question

difference between a positive integer and its reciprocal is -3/2 then find the number

Answer 1

let positive integer be x
then
x-(1/x)=-3/2
(x^2-1)/x=-3/2
then by cross multiplying the denominators
2x^2-2=-3x
2x^2+3x-2=0
by factorization
2x^2+4x-x-2=0
2x(x+2)-1(x+2)=02values of x are
1/2 & -2
but number is positive so x is 1/2

Answer 2

Hey friend,


Here is your answer,

Let that no. be 'x'

Now, according to the condition

=> x - (1/x) = -3/2
=> x^2 - 1 = -3x/2
=> x^2 + 3x/2 - 1 = 0
=> 2x^2 + 3x - 2 = 0 (quadratic equation)
=> 2x^2 + 4x - x - 2 = 0
=> 2x(x + 2) -1(x + 2) = 0
=> (2x - 1)(x + 2) = 0
=> x = 1/2 or x = -2

Since, the question asks for a positive integer, hence the positive integer is 1/2.


Hope it helps you.
Thank you.