the sum of two natural nos. is 8.determine the nos,.,if the sumof their reciprocals is 8/15?

Question

mention all steps

Answer 1

x + y = 8
(1/x) + (1/y) = 8/15

Two equations, two unknowns. Using substitution, since y = 8 - x,

(1/x) + (1/[8 - x]) = 8/15

Multiply both sides by 15x(8 - x),

15(8 - x) + 15x = 8x(8 - x)

120 - 15x + 15x = 64x - 8x^2

Move everything to the left hand side,

8x^2 - 64x + 120 = 0

Divide everything by 8,

x^2 - 8x + 15 = 0

And factor.

(x - 5)(x - 3) = 0

This means x = 5 or x = 3.
When x = 5, y = 3.
When x = 3, y = 5.

Your two numbers are 3 and 5.

Answer 2

1. Find rational numbers, which reciprocals are natural numbers: 1/15, 3/15, 5/15, 10/15, 15/15.
2. The only possible addition to 8/15 = 3/15 + 5/15
3. The reciprocals of this addition: 15/3 + 15/5 = 5/1 + 3/1 = 8
-> So the natural nos must be 5 and 3

Answer 3

Let the numbers be x and y.
x+y=8
1/x+1/y=8/15
=>(x+y)/xy=8/15
=>8/xy=8/15
=>xy=15
We know that(x-y)^2
=(x+y)^2-4xy
=8^2-4*15
=64-60
=4
Hence x-y=2
x+y=8
x- y=2
(Adding ) 2x=10
hence x=5
Putting the value x in x+y=8,we get y=3
therefore the numbers are 3 and 5

Answer 4

Start by saying that one number is n and therefore the other is
8 - n. Write their reciprocals in algebra and add them (over common denominator) and then equate this to 8/15. Solve for n. Try to use this help to do it yourself rather than copying any answer here. (Note I have seen too many wrong answers posted on this website.)

Answer 5

a+b=8
1/a+1/b=8/15
The second equation can be simplified as (b+a)/ab=8/15
Therefore, b=5 and a=3 would have these properties.

Answer 6

The no. are:-
3
5