Question

Find two numbers whose sum is 27 and product is 182?
Please give me an idea to this question pleaseeeeee.......

Answer 1

Let the two numbers be a and b.

So,
a+b = 27
ab = 182

Now,
(a+b)^2 = 27^2

a^2 + b^2 + 2ab = 729
a^2 + b^2 = 729 - 2ab
a^2 + b^2 = 729 - 364.
a^2 + b^2 = 365
a^2 + b^2 - 2ab = 365 - 2ab
(a-b)^2 = 365 - 364.
(a-b) = √ 1
a-b = +- 1......2nd eqn

a + b = 27.....1st eqn

Now solving the eqns 1 & 2
We get
if we take a - b = +1

a+b = 27
a-b = 1
_________
2a = 28
a = 14 & b = 13

And similarly if we take
a - b = -1

Then we get a = 13 and b = 14.

Answer 2

Let the two numbers be x and y.

Given that their sum = 27.

x + y = 27

Given that their product = 27.

xy = 182

x = 182/y  ----- (2)

Substitute (2) in (1), we get

182/y + y = 27

182 + y^2 = 27y

y^2 - 27y + 182 = 0

y^2 - 13y - 14y + 182 = 0

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

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

y = 13 (or) 14.

When x = 13,

Then x + y = 27

          x + 13 = 27

          x = 27 - 13

          x = 14.


When y = 14

Then x + y = 27

          14 + y = 27

           y = 27 - 14

           y = 13.


Therefore the two numbers are 13 and 14.


Verification:

13 + 14 = 27

13 * 14 = 182.


Hope this helps