Question

Answer the following
25. The sum of two numbers is 27 and their product is 182. Find those numbers.
OR​

Answer 1

Given

Sum of two numbers is 27 and product is 182

To Find

we have to find those numbers

$\sf\huge {\underline{\underline{{Solution}}}}$

Since , we don't know the numbers so let us assume some Variable :

let the first number be x

and the other number be y

according to the question:

sum of two numbers is 27

=> x+y= 27----(1)

And their product is 182

=>xy= 182----(2)

from equation 1

x = 27-y ----(3)

Now,put Equation 3 into Equation 2

=> (27-y)y= 182

=> 27y-y²=182

=> -y²+27y-182=0

=> y²-27y+182=0

=>y²-14y-13y+182=0

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

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

y= 13 or y = 14

At y = 13

x= 27-13= 14

At y = 14

x= 27-14= 13

Therefore, the numbers are either 13 ,14 or 14,13

Answer 2

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Let,

the first number be x

and the other number be y

according to the question:

sum of two numbers is 27

= x + y = 27---- (1)

And their product is 182

= xy = 182---- (2)

from equation 1

x = 27- y ---- (3)

Now,

From equation 2 and 3 -

= (27-y)y = 182

= 27y-y² = 182

= -y² + 27y - 182 = 0

= y² - 27y + 182 = 0

= y² - 14y - 13y + 182 = 0

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

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

y = 13 or y = 14

At y = 13

x = 27 - 13 = 14

At y = 14

x = 27-14

x = 13

Therefore, the numbers are either 13 ,14 or 14,13

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