The sum of two number is 12 if the sum of their reciprocal is3_5 FIND NUMBER
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Answered by
4
Hey there !!
Let the required numbers be x and y.
Then,
→ x + y = 12............(1) .
And, the sum of its reciprocal :-
→
⇒
⇒
⇒ 3xy = 12 × 5 .
⇒ 3xy = 60 .
⇒ xy = 60/3 .
⇒ xy = 20.
Now, using identity :-
→ ( x - y )² = ( x + y )² - 4xy .
∴ ( x - y ) =
⇒ x - y =
⇒ x - y = √(144 - 80 ) .
⇒ x - y = √(64) .
⇒ x - y = 8..........(2).
On substracting the equation (1) and (2), we get
x + y = 12.
x - y = 8.
- + -
________
⇒ 2y = 4 .
∴ y = 2 .
Putting the value of y in equation (1), we get
⇒ x + 2 = 12.
⇒ x = 12 - 2 .
∴ x = 10 .
Hence, the required number are 10 and 2 .
THANKS
#BeBrainly.
Let the required numbers be x and y.
Then,
→ x + y = 12............(1) .
And, the sum of its reciprocal :-
→
⇒
⇒
⇒ 3xy = 12 × 5 .
⇒ 3xy = 60 .
⇒ xy = 60/3 .
⇒ xy = 20.
Now, using identity :-
→ ( x - y )² = ( x + y )² - 4xy .
∴ ( x - y ) =
⇒ x - y =
⇒ x - y = √(144 - 80 ) .
⇒ x - y = √(64) .
⇒ x - y = 8..........(2).
On substracting the equation (1) and (2), we get
x + y = 12.
x - y = 8.
- + -
________
⇒ 2y = 4 .
∴ y = 2 .
Putting the value of y in equation (1), we get
⇒ x + 2 = 12.
⇒ x = 12 - 2 .
∴ x = 10 .
Hence, the required number are 10 and 2 .
THANKS
#BeBrainly.
Answered by
1
Let that two numbers be x and y
According to question,
Sum of numbers = 12
x + y = 12
y = 12 - x .......................i)
And,
Sum of their reciprocal = 3
Putting y = 12 -x,
Hence,
Numbers are 10 and 2
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