Question

Find the decimal numbers whose sum is 2 and product is-0.75

Answer 1

Let x & y be the 2 decimal numbers

By given condition,

x + y = 2...(1)

x × y = 0.75

y = 0.75/x...(2)

Substituting (2) in (1),

x + 0.75/x = 2

Multiplying by x on both sides,

x² + 0.75 = 2x

x² - 2x + 0.75 = 0

0.75 = 3/4

Thus, 

4x² - 8x + 3 = 0

(2x-1) (2x-3) = 0

Thus, x = 1/2 or 3/2

In decimals, x = 0.5 or 1.5

Thus, y = 1.5 or 0.5

Answer 2

Solution :-

Let 'x' and 'y' be the two decimal numbers respectively.

Therefore, according to the question.

x + y = 2 

⇒ x = 2 - y ...............(1) 

xy = 0.75 ...............(2)

Now, substituting (1) in (2), we get.

⇒ (2 - y)*(y) = 0.75

⇒ 2y - y² = 0.75

⇒ y² - 2y + 0.75 = 0 

Multiplying y² - 2y + 0.75 by 4, we get.

⇒ (y² - 2y + 0.75 = 0)*4

⇒ 4y² - 8y + 3 = 0

⇒ 4y² - 6y - 2y + 3 = 0

⇒ 2y(2y - 3) - 1(2y - 3) = 0

⇒ (2y - 1) or (2y -3) = 0

⇒ 2y = 1   or   2y = 3

⇒ y = 1/2  or  y = 3/2

Therefore, in decimals y = 0.5 or 1.5 

and, x = 1.5 or 0.5

Answer.