The sum of two number is 8 and the sum of their recipocal is 8/15 find the number
Answers
Suppose the first number is x
Since sum of two numbers = 8
=> Other number = (8 - x)
We know that for any number x,
reciprocal of x = 1/x
a/c to question
1/x + 1/(8 - x) = 8/15
=> (8 - x + x)/(x)(8 - x) = 8/15
=> 8/(8x - x^2) = 8/15
=> 8x - x^2 = 15
=> x^2 - 8x + 15 = 0
=> x^2 - 5x - 3x + 15 = 0
=> x(x - 5) - 3(x - 5) = 0
=> (x - 3) (x - 5) = 0
=> x = 3 or x = 5
=> 8 - x = 8 - 3 = 5 (if x = 3)
=> 8 - x = 8 - 5 = 3 (if x = 5)
Answer:
3 , 5
Explanation:
Suppose the first number is x
Since sum of two numbers = 8
=> Other number = (8 - x)
We know that for any number x,
Reciprocal of X = 1/X
According to the question,
1/x + 1/(8 - x) = 8/15
=> (8 - x + x)/(x)(8 - x) = 8/15
=> 8/(8x - x^2) = 8/15
=> 8x - x^2 = 15
=> x^2 - 8x + 15 = 0
=> x^2 - 5x - 3x + 15 = 0
=> x(x - 5) - 3(x - 5) = 0
=> (x - 3) (x - 5) = 0
=> x = 3 or x = 5
=> 8 - x = 8 - 3 = 5 (if x = 3)
=> 8 - x = 8 - 5 = 3 (if x = 5)
The two no. are 3&5.