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

Answer:

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.

Explanation:

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

we get,

$\frac{1}{t}+\frac{1}{t+2}=\frac{15}{112}$

On solving the above equation, we get

$\frac{t+t+2}{t^2+2t}=\frac{15}{112}$$112(2t+2)=15(t^2+2t)$$224t+224=15t^2+30t$

$15t^2-194t-224=0$$t=\frac{194\pm\sqrt{37636+13440}}{30}$$t=\frac{194\pm\sqrt{51076}}{30}$$t=\frac{194\pm226}{30}$$t=14,-\frac{32}{30}$

Possible t value is 14.

The required integers are 14 and 16.

Answer is:

$\frac{1}{t}+\frac{1}{t+2}=\frac{15}{112}$

The required integers are 14 and 16.