solve this??

Question

The sum of the reciprocal of an intezers and 3 times of the next higher is 11/24,find the reciprocal intezer.

Answer 1

Sorry i'm going to bed. Wish i could help

Answer 2

Let x = the integer
the reciprocal = 1/x
next higher integer = x + 1

The sum of the reciprocal of an integer and 3 times the next higher is 11/24

1/x + 3(x + 1) = 11/24

Distribute the 3.
1/x + 3x + 3 = 11/24

Multiply each term by 24x (the LCD of both fractions)
24 + 72x^2 + 72x = 11x

Subtract 11x from both sides.
72x^2 + 61x - 24 = 0

This trinomial doesn't have rational roots, so you won't get an integer as an answer. Are you sure you have the correct problem?

Answer 3

The sum of the reciprocal of an integer and 3 times the next higher integer is 11/24.

X = the integer
1/X = the reciprocal
X + 1 = the next integer

3(x + 1) + (1/x) = 11/24
3x + 3 + 1/x = 11/24
3x^2 + 3x + 1 = 11x/24
3x^2 + (72/24 - 11/24)x + 1 = 0
3x^2 + 61x/24 + 1 = 0
x^2 + 61x/72 + 1/3 = 0
x^2 + 61x/72 + 3721/20736 = -3091/20736
(x + 61/144)^2 = -3091/20736
x + 61/144 = +/- sqrt(-3091)/144
x = -61 +/- sqrt(-3091)/144

Your answer involves the square root of a negative number (i.e., not a real number).

Good luck with that one!

Answer 4

If x = the integer, (x+1) is the next higher and their reciprocals are 1/x and 1/(x+1)

1/x + 1/(x+1) = 11/24

Multiply all 3 by the common denominator 24x(x+1)

This gives 24(x+1) + 24x = 11x(x+1)

Do this out, make it equal to zero, then solve by FOIL if possible or by the quadratic formula.

Answer 5

1/x + 3(x + 1) = 11/24
24/x + 72x + 72 = 11
24 + 72x^2 + 72x = 11x
72x^2 + 61x + 24 = 0
x = -61 ± √( 3721 - 6912))/144
t'ain't no such integer!

Let's try
1/x + 3/(x + 1) = 11/24
24/x + 72/(x + 1) = 11
24x + 24 + 72x = 11x^2 + 11x
11x^2 - 85x - 24 = 0
x = (85 ± √(7225 + 1056))/22
x = (85 ± √(8281))/22
x = (85 ± 91)/22
x = 8, -0.272727...
The integer is 8
check:
1/8 + 3/9 = (9 + 24)/72 = (3 + 8)/24 = 11/24