Question

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

Answer 1

Solution:-
Let the one number be 'x'
So, its reciprocal will be 1/x
Now, according to the question.
x + 1/x = 61/30
(x² + 1)/x = 61/30 after cross multiplying, we get
30x² + 30 = 61x
30x² - 61x + 30 = 0
30x² - 36x - 25x + 30 = 0
6x(5x - 6) - 5(5x - 6) = 0
(6x - 5) (5x - 6) = 0
6x = 5
x = 5/6
And,
5x = 6
x = 6/5
So, the numbers are 5/6 and 6/5
Answer.

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the required number be x.

Then,

According to the Question,

⇒ x + 1/x = 2(1/30)

⇒ x² + 1/x = 61/30

⇒ 30x² + 30 = 61x

⇒ 30x² - 61x + 30 = 0

By using factorization method, we get

⇒ 30x² - 61x + 30 = 0

⇒ 30x² - 36x - 25x + 30 = 0

⇒ 6x(5x - 6) - 5(5x - 6) = 0

⇒ (5x - 6) (6x - 5) = 0

⇒ 5x - 6 = 0 or 6x - 5 = 0

⇒ x = 5/6, 6/5

Hence, the required number is 5/6 and 6/5.