Question

find two numbers whose sum is 27and proud is182​

Answer 1

Answer:

( what do you mean by proud )

x = 13, 14

y = 13, 14

hope it helps u :-) ✌

Answer 2

$\huge\underline\mathfrak{Question-}$

Find two numbers whose sum is 27 and product is 182.

$\huge\underline\mathfrak{Solution-}$

Let the number be x and y.

Sum of numbers = 27

: $\implies$ $\huge{\boxed{\mathrm{\red{x+y=27}}}}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(1)

Product of numbers = 182

: $\implies$ $\huge{\boxed{\mathrm{\red{xy=182}}}}$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(2)

From (1), we get,

x = 27 - y

Put the value of x in (2),

: $\implies$ (27-y)(y) = 182

: $\implies$ 27y - y² = 182

: $\implies$ y² - 27y + 182 = 0

By splitting middle term,

Sum = -27

Product = 182

factors = (-13, -14)

: $\implies$ y² - 14y - 13y + 182 = 0

: $\implies$ y (y - 14) -13 (y - 14) = 0

: $\implies$ (y - 14)(y - 13) = 0

: $\implies$ y = 14, 13

Now put y = 14, 13 one by one in equation (1).

$\boxed{\green{When\:y=14}}$

: $\implies$ x + 14 = 27

: $\implies$ x = 27 - 14

: $\implies$ x = 13

$\boxed{\green{When\:y=13}}$

: $\implies$ x + 13 = 27

: $\implies$ x = 27 - 13

: $\implies$ x = 14

So, we get two values of x and y.

When y = 13, x = 14

When y = 14, x = 13