Question

Hello could you help me solve this problem (Week 27 Practice t #1) -The sum of the reciprocals of two consecutive even integers is 15/112. Write an equation that can be used to find the two integers. Find the two integers.

Answer 1

Given that,

The sum of the reciprocals of two consecutive even integers is 15/112.

To find the equation that can be used to find the two integers.

Step-by-step explanation:

Let the two consecutive even integers be t and t+2

we get,

`(1)/(t)+(1)/(t+2)=(15)/(112)`

On solving the above equation, we get

`(t+t+2)/(t^2+2t)=(15)/(112)`
`112(2t+2)=15(t^2+2t)`
`224t+224=15t^2+30t`

`15t^2-194t-224=0`
`t=(194\pm√(37636+13440))/(30)`
`t=(194\pm√(51076))/(30)`
`t=(194\pm226)/(30)`
`t=14,-(32)/(30)`

Possible t value is 14.

The required integers are 14 and 16.

Answer is:

`(1)/(t)+(1)/(t+2)=(15)/(112)`

The required integers are 14 and 16.