Question

Difference between a positive integers and it's reciprocal is 3/2 ,then find the number.​

Answer 1

Answer:

= 1/2

Step-by-step explanation:

et 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

$x - \frac{1}{x} = \frac{3}{2} \\ \\ = > \frac{ {x}^{2} - 1 }{x} = \frac{3}{2} \\ \\ = > 2 {x}^{2} - 2 = 3x \\ \\ = > 2 {x}^{2} - 3x - 2 = 0\\ \\ = > 2 {x}^{2} - 4x + x - 2 = 0 \\ \\ = > 2x( x - 2) + 1(x - 2) = 0 \\ \\ = > (x - 2)(2x + 1) = 0$

Required values of x : 2 and -1/2

Since negative value is not acceptable hence the correct value of x will be 2

So, the number will be 2 ✔

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Hope it helps ☺

Fóllòw Më ❤