Two consecutive even whole numbers are selected. the difference between the reciprocals of the two numbers is 1/40. determine the two numbers

2 numbers could be 10 and 12 

or - 12 and - 10 

Step-by-step explanation:

let the 2 numbers be x and x + 2

since they are 2 consecutive even numbers, the difference between them is 2

the difference between the reciprocals is 1/60 

we have to mulitply the 2 denominators x and (x+2) to get a common denominator for the 2 fractions 

= 

we can then remove the brackets from the numerator and denominator 

and then cross multiply

60 * 2 = x² + 2x

120 = x² + 2x

x² + 2x - 120 = 0

we have a quadratic equation which needs to be solved 

x² + 12x - 10x - 120 = 0

x (x + 12) - 10(x + 12) = 0

(x - 10) (x + 12) = 0

x - 10 = 0     or   x + 12 = 0

x = 10                x = -12

answer: 0,6

step-by-step explanation:

this would make it the y intercept.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4