Question

The sum of two numbers is 9 and the sum of their reciprocals is ½. Find the numbers.
(Class 10 Maths Sample Question Paper)

Answer 1

SOLUTION:

GIVEN:
Sum of two numbers = 9
Sum of their reciprocals = 1/2
Let one number be x and other number will be (9 - x).

ATQ

1/x + 1 / (9-x) = ½
9 - x +x / x (9-x) = ½
9  × 2 = x (9-x)
18 = 9x -x²
x² - 9x +18= 0

x² -6x -3x +18= 0
x(x-6) -3(x-6)= 0
(x-6) (x-3) = 0
x-6= 0 or x -3 = 0

x = 6 or x = 3

Hence, the numbers are 3 and 6.

HOPE THIS WILL HELP YOU...

Answer 2

HELLO DEAR


LET THE ONE NO. BE X

THEN THE ANOTHER NO. BE (9-X)
$\frac{1}{x} + \frac{1}{(9 - x)} = \frac{1}{2} \\ = > \frac{9 - x + x}{x(9 - x)} = \frac{1}{2} \\ = > \frac{9}{(9x - {x}^{2} )} = \frac{1}{2} \\ = > 18 = 9x - {x}^{2} \\ = > {x}^{2} - 9x + 18 = 0\\ = > {x}^{2} - 6x - 3x + 18 = 0 \\ = > x(x - 6) - 3(x - 6) \\ = > (x - 3)(x - 6) \\ = > x = 3 \: \: and \: \: \: x = 6$

I HOPE ITS HELP YOU DEAR,
THANKS