Question

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

Answer 1

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

12x²+12=25x

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

 12x²+12-25x=25x-25x

 12x²-25x+12=0

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




where a=12, b=-25, and c=12.

Answer 2

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