The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers. Find the two integers.

Question

anonymous · Answer

attachment

anonymous · Answer

@DemolisionWolf

campbell_st · Answer

start with the basics

the consecutive even integers are 

x and x + 2

their reciprocals are 

$$\frac{1}{x} ...and.... \frac{1}{x + 2}$$

then using the sum you have 

$$\frac{1}{x} + \frac{1}{x + 2} = \frac{7}{24}$$

so this requires a common denominator on the left

$$\frac{(x +2) + x}{x(x+2)} = \frac{7}{24}$$

simplify and cross multiply and you get 

$$24(2x + 2) = 7(x^2 + 2)$$

which becomes 

$$7x^2 - 34x -48 = 0$$

so the quadratic... for x.... and you'll have the value for x....

I'd recommend the general quadratic formula... 

only use the answer for the positive even integer... 

hope it helps

anonymous · Answer

i put the wrong attachment :O @campbell_st its this one

campbell_st · Answer

I know... the method I used will get the answer for you...

anonymous · Answer

i got A is that correct? @campbell_st

campbell_st · Answer

well what value do you get for the integer x

as the 2nd integer is x + 2