Question

find two no. whose sum is 27 and product is 182​

Answer 1

Answer:

• The required numbers are 13 & 14.

Step-by-step explanation:

Let required numbers be x and y .

By given condition , We have:

• x + y = 27
• xy = 182

Step: Solve the equations.

x + y = 27

→ x = 27 - y ......(i)

Step : Put the value of x in equation (ii)

→ xy ..(Equation)

→ (27 - y)y = 182

→ 27y - y² = 182

→ - ( y² - 27y + 182) = 0

→ y² - 27y + 182 = 0

→ y² - 13y - 14y - 182 = 0

→ y(y - 13) - 14(y - 13) = 0

→ ( y - 13) ( y - 14) = 0

So, Value of y = 13 0r 14

Step: Put the value of y in equation (i)

→ x = 27 - y

→ x = 27 - 13

→ x = 14

Therefore, the required numbers are 13 & 14.

Answer 2

let the first number be x and second no be y

so according to question

x+y=27. _ eq 1

x×y =182. _ eq 2

by eq 1

x= 27-y

subtitude it in eq 2

(27-y)(y) = 182

27y - y^2 =182

-y^2 +27y -182

now split the middle term

-y^2 +13y+ 14y -182

y(-y+13) -14(y+13)

(y-14)(y+13) =0

so y =14 or -13

let y = 14

subtitude in eq 1

x+14 = 27

x= 13

let y= -13

subtitude in eq 1

x+(-13)= 27

x= 50

answer x = 13, y= 14

or x= 50 , y = -13