The sum of 2 numbers is 8 and 15 times the sum of their reciprocals is also 8 . Find the number.?

Question

Answer

Let the no.s are 'a' and b'

a+b = 8

15(1/a + 1/b) = 8

15(a+b) = 8ab
ab = 15

here now form quadratic who's zeroes are a and b

which is
x²-8x+15 = 0

x = [8±√[64-60]]÷2
= [8±√4]/2
= 4±1

then a and b are
3 and 5

no.s are
3 and 5

Answer

Problem Statement

The sum of 2 numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.

Solution

Let the two numbers be x and y.

According to the problem statement:

x + y = 8 ------(1)

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

1/x + 1/y = 8/15 ------(2)

Now, we need to solve these two equations (equation 1 and equation 2) to get the values of x and y.

Let's simplify equation 2:

1/x + 1/y = 8/15

(x + y)/xy = 8/15

Substituting the value of x + y from equation 1:

8/xy = 8/15

xy = 15 ------(3)

Using equation 1 and equation 3, we can solve for x and y:

x + y = 8

xy = 15

Substituting y = 8 - x in the second equation:

x(8 - x) = 15

8x - x^2 = 15

x^2 - 8x + 15 = 0

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

So, the two numbers are either 3 and 5 or 5 and 3.

Therefore, the numbers are 3 and 5.

Final Answer

The two numbers are 3 and 5.

Answer

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