Question

The sum of the reciprocals of two consecutive even integers is 9/40. Find the integers. smaller integer larger integer

Answer 1

Smaller integer is 8, larger one is 10.

Explanation:

Let one integer be x then the other is x+2, so from the given information:

1 /x + 1 / x+2 = 9/40

Multiply through by 40x(x+2);

40(x + 2) + 40x = 9x(x + 2)

80x + 80 = 9x^2 + 18x

9x^2 - 62x - 80 = 0

(9x + 10)(x - 8) = 0

x = 8, -1.1111

x must be 8 so the other one is 8+2 = 10.

Answer 2

8 and 10

Explanation:

2x and 2x+2 the integers

• 1/2x+1/(2x+2)= 9/40
• 1/x+1/(x+1)=9/20
• (x+x+1)/(x*(x+1))= 9/20
• 9x²+9x= 20(2x+1)
• 9x²-31x-20=0
• x= 4 integer solution

So the numbers are 8 and 10