Question

find two numbers whose sum is 30 and product is 225?

Answer 1

Method — 1


Using two variables : -


Let the required numbers are x and y.

According to the question, their sum is 30

So, x + y = 30

x = 30 - y ------: ( 1 )



Also given that thier product is 225.

xy = 225


Substituting the value of x from ( 1 )


( 30 - y )y = 225

30y - y² = 225

y² - 30y + 225 = 0

y² - 2( 15 × y ) + ( 15 )² = 0

( y - 15 )² = 0

y - 15 = 0

y = 15




Therefore, numbers are :

y = 15
x = 30 - y = 30 - 15 = 15





Method — 2


Let numbers are x and ( 30 - x ),


Given, their product = 225

x( 30 - x ) = 225

30x - x² = 225

x² - 30x - 225 = 0

( x - 15 )² = 0

x - 15 = 0

x = 15



Therefore, numbers are :

x = 15

y = 30 - 15 = 15





Therefore, numbers satisfying the question are 15 and 15
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Answer 2

Concept

A variable is any quantity which can have some value. It can be anything.

Given

Sum of numbers=30

Product=225

To find

Numbers whose sum is 30.

Explanation

let the first number be x

because the sum is 30 so the second number will be 30-x

We have to find the product of numbers:

x(30-x)=225

30x-$x^{2}$=225

$x^{2} -30x+225=0$

$x^{2}$-15x-15x+225=0

x(x-15)-15(x-15)=0

(x-15)(x-15)=0

x=15

So the first number will be 15 And the second number will also be 15 because the sum is 30.

Hence both numbers are 15.

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