the denominator of a fraction is 3 more than its numerator the sum of the fraction and its reciprocal is 2 9/10find the fraction
Answers
Answer:
He inculcates good values in me.
There is cow. Which daily comes to my
home.
He feeds the cow.
He laughs wholeheartedly.
He cracks jokes.
He has good sense of humour.
He keeps peanuts in his pocket.
He keeps dry fruits in his pocket.
At times he gives me money stealthily.
He gets angry once in a blue moon
(rarely).
(I confide in my grandpa.)
He does not tell a lie.
He does not wake up late.
Step-by-step explanation:
Given :-
The denominator of a fraction is 3 more than its numerator the sum of the fraction and its reciprocal is 2 9/10.
To find :-
Find the fraction ?
Solution :-
Let the numerator of a fraction be X
Then , the denominator = is 3 more than its numerator
=> Denominator= Numerator+3
=> Denominator = X+3
Then , the fraction = Numerator/ Denominator
The fraction = (X+3)/X ---------(1)
The reciprocal of the fraction
= X/(X+3) -----(2)
On adding (1)&(2) then
=>[ (X+3)/X ] + [ X/(X+3) ]
=>[ (X+3)(X+3) + (X)(X) ]/[X(X+3)]
=> [(X+3)²+X²]/(X(X+3))
=> (X²+6X+9+X²)/(X²+3X)
=> (2X²+6X+9)/(X²+3X)
According to the given problem
The sum of the fraction and its reciprocal = 2 9/10 = 29/10
=> (2X²+6X+9)/(X²+3X) = 29/10
On applying cross multiplication then
=> 10(2X²+6X+9) = 29(X²+3X)
=> 20X²+60X+90 = 29X²+87X
=> 20X²+60X+90 -29X²-87X= 0
=> -9X²-27X+90 = 0
=> -9(X²+3X-10) = 0
=> X²+3X-10 = 0/-9
=> X²+3X-10 = 0
=> X²+5X-2X-10 = 0
=> X(X+5)-2(X+5) = 0
=> (X+5)(X-2) = 0
=> X+5 = 0 or X-2 = 0
=> X = -5 or X = 2
On taking positive value for X = 2
Numerator = 2
Denominator = 2+3 = 5
Fraction = 2/5
Answer:-
The required fraction for the given problem is 2/5
Check:-
The fraction = 2/5
Denominator = 2+3 = Numerator+3
And
Reciprocal of 2/5 = 5/2
=> Their sum = (2/5)+(5/2)
=> (4+25)/10
=> 29/10
=> 2 9/10
The sum of the fraction and its reciprocal = 2 9/10
If we take X = -5 we get same value
Verified the given relations in the given problem