Question

If the sum of two numbers be multiplied by each
separately the products, so obtained are 2418 and
3666. Find the numbers.​

Answer 1

$\bold{\boxed{Answer}}$

Let the number be x and y.

Now, according to the question,

x(x + y) = 2418 - - - - - - - - - - (i)

and y(x + y) = 3666 - - - - - - (ii)

On adding Eqs. (i) and (ii), we get

x2 + xy + yx + y2 = 6084

⇒ x2 + 2xy + y2 = 6084

⇒ (x + y)2 = 6084

∴ x + y = √6084 = 78 --------(iii)

On subtracting Eq. (ii) from Eq. (i), we get

x2 + xy - yx - y2 = -1248

⇒ x2 - y2 = -1248

⇒ (x + y) (x - y) = -1248

⇒ 78(x - y) = -1248

⇒ x - y = - 1248 / 78 = -16

⇒ (y - x) = 16 - - - - - (iv)

From (iii) and (iv),

x = 47

y = 31

Answer 2

47,31 is the answer for questions