# The sum of a number and its reciprocal is 65/28 find the number

2
by Tanytifuminirataze

2016-02-13T20:48:08+05:30
1.  Let x be the number and 1/x be its reciprocal.

2.  Then,  since the sum of a number and its reciprocal is 25/12.
x+1/x=25/12

3.  Multiply 12x to both sides of the equation to get rid of the denominators.

12x(x+1/x)=12x.25/12

12x
²+12=25x

4.
Subtract 25x to put the equation in quadratic form

12x
²+12-25x=25x-25x

12x
²-25x+12=0

5.
We can use the quadratic formula given as  (its given in the file)

where a=12, b=-25, and c=12.
but, according to me x (the number) = 1.75
1.75 + 1/1.75 (0.57...) = 65/28 (2.32....)......
sry i did d ques wrong
instead of puttin 65/28 i put 25/12
its ok....
• Brainly User
2016-02-13T20:55:42+05:30
Let the no. be x and other be 1/x..so according to the question... x+1/x=65/28...x^2+1/x=65/28=>28x^2+28=65x..=>28^2-65x+28=0=>28^2-49x-16x+28=0=>7x(4x-7)-4(4x-7)=0=>(4x-7)(7x-4)=0==>x=7/4=1.75 and x=4/7=0.571
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correct ans...jhaisha...