Question

the sum of two no. is 5 and the sum of their squares is 14 than their product is equal to​

Answer 1

Answer:

Let the numbers be x and y.

Given

x + y = 5

and

$x {}^{2} + y {}^{2} = 14$

We have to find xy

We know

$(x + y) {}^{2} = x {}^{2} + y {}^{2} + 2xy \\ 5 {}^{2} = (x {}^{2} + y {}^{2} ) + 2xy \\ 25 = 14 + 2xy \\ 25 - 14 = 2xy \\ 11 = 2xy \\ \frac{11}{2} = xy \\ 5.5 = xy \\ xy = 5.5$

Answer 2

Given :

The sum of two no. is 5 and the sum of their squares is 14.

To find :

Product of numbers.

Solution :

Let the two numbers be 'a' and 'b'

∴ a + b = 5         _(1)

∴ a² + b² = 14        _(2)

∵ a² + b² = (a + b)² - 2ab

Now from (2) :

⇒ (a + b)² - 2ab = 14

⇒ 5² - 2ab = 14

⇒ 25 - 2ab = 14

⇒ 25 - 14 = 2ab

⇒ 11 = 2ab

⇒ ab = 11/2

∴ Product of two numbers = 11/2