Question

The sum of two numbers is 15 and the sum of their reciprocal is 3/10. Find the numbers.

Answer 1

let the two numbers are X and y
X+Y=15.....................(1)
SUMOF RECIPROCAL OF THAT TWO NUMBER=>1/X+1/Y=3/10
=>X+Y/XY = 3/10
=>X+Y = 3XY/10...........................(2)
SUBSTITUTE X+Y VALUE  IN (2)
=>15*10 = 3XY
=>150 = 3XY
=>50=XY
=>Y=50/X..........................(3)
(3) IN (1)
X+50/X=15
X²+50=15X
X²-15X+50=0
X²-5X-10X+50=0
X(X-5)-10(X-5)=0
(X-10)(X-5)=0
X=10 AND X=5
SUBSTITUTE X VALUE IN (1)
10+Y=15 AND 5+Y=15
Y=5 AND Y=10

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the 1st natural number be x.

And the 2nd natural number is (15 - x).

Sum of their reciprocals = 3/10

According to the Question,

⇒ 1/x + 1/(15 - x) = 3/10

⇒ 15/(15x - x²) = 3/10

⇒ 150 = 45x - 3x²

⇒ 3x² - 45x + 150 = 0

⇒ x² - 15x + 50 = 0

⇒ x² - 5x - 10x + 50 = 0

⇒ (x - 10) (x - 5) = 0

⇒ x - 10 = 0 or x - 5 = 0

⇒ x = 10, 5

When x = 10

1st number = x = 10

2nd number = 15 - x = 15 - 10 = 5

When x = 5

1st number = x = 5

2nd number = 15 - x = 15 - 5 = 10

Hence, the numbers are 10 and 5 or 5 and 10.

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