Question

The sum of a number and its reciprocal is 17/4. The number is :

Answer 1

Given x+1/x=17/4
So,x^2+1/x=17/4
4 (x^2+1)=17x
4x^2+4=17x
4x^2-17x+4=0
If you factorise the equation you will get the value of x.
Hope it helps you......

Answer 2

Let the no. be x
Then it s reiprocal will be 1/x.
According to question...
x + 1/x = 17/4
x²/x + 1/x = 17/4
x²+ 1 = 17x/4
x²-17x/4+ 1 = 0
Multiply whole eqn with 4, we get
4x²-17x+4=0
4x²-(16 + 1)x +4=0
4x²- 16x - x + 4=0
4x (x-4) -1 (x-4)=0
(4x - 1) ( x -4 )=0
x =1/4 or x = 4