Question

plz help me in this.

the sum of a number and it's reciprocal be26/5.Find the numbers.

Answer 1

X=1
X=25

Hope it will help you

Answer 2

Let the number be 'X'
Given,
X + 1/X = 26/5
(X^2 + 1)/X = 26/5
(X^2 + 1) * 5 = 26*X
5X^2 - 26X + 5 = 0

Roots(quadratic formula): [-b +-Rt(b^2 - 4ac)]/2a
[26 +- rt(676 - 4*5*5)]/2*5
= [26 +- rt(576)]/10 = [26 +- 24]/10 = 50/10 or 2/10 = 5 or 1/5
Hence the number is '5'..(it can also be 1/5)

Alternatively:
26/5 = 5 1/5 [fractions]
Now: 5 1/5 = 5 + 1/5... [coz 5 1/5 = 26/5...... 5 1/5 = (5*5 + 1)/5 = 5 + 1/5]
Hence, our number is '5'