Question

Two consecutive odd whole numbers are selected. The difference between the reciprocals of the two numbers is 2/143. Determine the two numbers.

Answer 1

Answer:

The numbers are 11 and 13

Step-by-step explanation:

Let

the first odd whole number=x

Reciprocal=1/x

Second odd whole number=x+2

Reciprocal=1/x+2

The difference

(1/x) - 1/(x+2)=2/143

(x+2)-x / (x)(x+2)=2/143

x+2-x/x(x+2)=2/143

2/x(x+2)=2/143

2(143)=2(x^2+2x)

286=2x^2+4x

2x^2+4x-286=0

x^2+2x-143=0

Solve the quadratic Equation

x=-b +or- √b^2-4ac/2a

a=1

b=2

c=-143

x= -b +or- √b^2-4ac/2a

=-2 +or- √(2)^2-(4)(1)(-143) / 2(1)

= -2 +or- √4-(-572) / 2

= -2 +or- √4+572/2

= -2 +or- √576/2

= -2 +or- 24/2

x= -2+24/2

= 22/2

=11

Or

x= -2-24/2

= -26/2

= -13

Taking the positive value

x=11

The second odd whole number=x+2

=11+2

=13