The difference of two numbers is 4 if the difference of their reciprocals is 4 by 21 find the number
Answers
Finding the number
Answer: Two numbers can be 7 and 3 and Two numbers can be -3 and -7.
Explanation:
Given that difference of two number is 4
And difference of their reciprocal = 4/21
Need to find the numbers
let assume smaller number = x
As the difference of two number is 4 , if we add 4 to smaller number we will get bigger number that is x + 4
reciprocal of x = 1/x
reciprocal of x + 4 = 1/(x+4)
As difference of reciprocals = 4/21
⇒ 1/x - 1/(x+4) = 4/21
⇒ (x+4 - x) / (x² + 4x ) = 4/21
⇒ 4/( x² + 4x ) = 4/21
⇒ 4 × 21 = 4 ×( x² + 4x )
⇒ 21 = ( x² + 4x )
=> x² + 4x - 21 = 0
On splitting the middle term we get
x² + 7x -3x - 21 = 0
⇒x(x+7) - 3( x + 7) = 0
⇒(x - 3) ( x + 7) = 0
so x - 3 = 0 or x + 7 = 0
so x = 3 or x = -7
when x = 3 , x + 4 = 3 + 4 = 7
when x = -7 , x + 4 = -7 + 4 = -3
hence there are two possible sets of number for given scenarion.
two numbers can be 7 and 3 where 7 is greater number than 3 and other possiblity is two numbers are -3 and -7 where -3 is greater number that -7.
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