Question

the sum of two numbers is 25 and their product is 144. find the numbers

Answer 1

Answer:

Let

One number = x

other number = y

Sum

====

x+y=25

x=25-y...............(1)

Product

=======

xy=144...............(2)

Put the value of x in above equation

(25-y)y=144

25y-y^2=144

y^2-25y+144=0

y^2-16y-9y+144=0

y^2-16y-9y+144=0

y(y-16)-9(y-16)=0

(y-9)(y-16)=0

y-9=0 or y-16=0

y=9 or y=16

Put the value of y in (1)

x=25-16=9

x=25-9=16

So numbers are 9 and 16

Answer 2

✍ What Is Given ?

• The sum of two numbers is 25.
• Their product is 144.

✍ What we need to find ?

• The 2 numbers.

✍ Solution :-

Let one number be x.

Let another number be y.

So, As per Equation,

x + y = 25,

x × y = 144.

$\sf{x + y = 25}$

$\sf{y = 25 - x}$

Now, xy = 144. __________(eq. 1)

Put the value of x.

$\sf{y(25 - y) = 144}$

$\sf{25y - {y}^{2} = 144}$

We Can Write It As,

$\sf{ {y}^{2} - 25y - 144 = 0}$

Use Splitting Middle Term Method.

$\sf{ {y}^{2} - 16y - 9y - 144 = 0}$

Take Common.

$\sf{y(y - 16) - 9(y - 16) = 0 }$

$\sf{(y - 9)(y - 16) = 0}$

So, Y = 9 Or 16,

Put the values Of Y in (eq. 1)

xy = 144

9x = 144

x = 16.

So, Your Numbers Are 9 and 16.