Question

The sum of a no.and its reciprocal is 61/30 find no.

Answer 1

Let the number be x
And its reciprocal be 1/x
A/q
$x + \frac{x}{1} = \frac{61}{30}$
$\frac{ {x}^{2} + 1 }{x} = \frac{61}{30}$
By cross multiplication we get,
${30x^2} +30 = 61x}$
$30x^{2} - 61x + 30 = 0$
$30 {x}^{2} - 36x - 25x + 30 = 0$
$6x(5x - 6) - 5(5x - 6) = 0$
$(6x - 5)(5x - 6) = 0$
Now,
$6x = 5 \\ x = \frac{5}{6}$
And,
$5x = 6 \\ x = \frac{6}{5}$

Answer 2

Answer:

Step-by-step explanation:

Let a be the number, then by the question a+(1/a)=61/30

30*(a^2)-61a+30=0

30(a^2)-36a-25a+30=0

(6a-5)(5a-6)=0

a=5/6,6/5