Question

the sum of reciprocals of two consecutives even numbers is 7/24.​

Answer 1

Answer:

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Step-by-step explanation:

The sum of the reciprocals of two consecutive even numbers is 7/24.

Find the numbers.

Let smaller even integer = x

Then larger even integer = x + 2

"Reciprocal of" means "1 over"

1 1 7

--- + ----- = ----

x x+2 24

The LCD is 24x(x+2). Multiply through by that LCD

1 1 7

24x(x+2)�--- + 24x(x+2)�----- = 24x(x+2)�----

x x+2 24

Cancel what will cancel

1 1 7

24x(x+2)�--- + 24x(x+2)�----- = 24x(x+2)�----

x x+2 24

24(x+2) + 24x = x(x+2)�7

24x + 48 + 24x = (x�+2x)7

48x + 48 = 7x� + 14x

0 = 7x� - 34x - 48

0 = (7x + 8)(x - 6)

Set first factor = 0

7x + 8 = 0

7x = -8

x = -8/7

Set second factor = 0

x - 6 = 0

x = 6

Discard fraction answer. Solution: smaller = 6, larger = 6+2 or 8

Answer 2

Answer:

Let the no. be x and x+2.

Now their reciprocals=1/x and 1/x+2

According to question,

1/x+1/x+2=7/24

=)x+2+x/x^2+2x=7/24

=)2x+2/x^2+2x=7/24

=)48x+48=7x^2+14x

=)7x^2-34x-48=0

=)7x^2-42x+8x-48=0

=)7x(x-6)+8(x-6)=0

=)(x-6)(7x+8)=0

x=6 and 8/7