Question

the product of two number is 36 if their sum is 20
find the number​

Answer 1

Given:

• Product of two numbers is 36.
• The sum of two numbers is 20.

To Find:

• The value of those two numbers.

Concept Used:

• We will suppose those two numbers as unknown variables .
• Secondly we will convert the given statements into mathematical expression.

Solution:

Let us suppose the

• First number as x .
• Second number as y .

Statement 1 :

Firstly it is given that product of two number is 36 .

So , According to our suppposition ,

$\sf{\implies x\times y =36.}$

${\underline{\red{\sf{\leadsto x =\dfrac{36}{y}}}}}$ ..................(1)

Statement 2:

Then it is given that their sum is 20 .

So , According to statement ,

$\sf{\implies x+y = 20}$ ...............(2)

$\rule{200}1$

Now , Putting the value of (1) into (2) ,we get;

$\sf{\implies y+\dfrac{36}{y}=20}$

$\sf{\implies \dfrac{y^{2}+36}{y}=20}$

$\sf{\implies y^{2}+36=20y}$

$\sf{\implies y^{2}-20y+36=0}$

$\sf{\implies y^{2}-2y-18y+36=0}$

$\sf{\implies y(y-2)-18(y-2)=0}$

$\sf{\implies (y-2)(y-18)=0}$

${\underline{\boxed{\red{\sf{\leadsto x =2,18}}}}}$

We have now got 2 values of y which are 2 and 18 respectively.

So, there will be two values of x also .

Taking y =2 ,

$\sf{\implies 2+x=20}$

$\sf{\implies x=20-2}$

${\underline{\red{\sf{\leadsto x=18}}}}$

So, one value of x is 18 .

Taking y =18,

$\sf{\implies 18+x=20}$

$\sf{\implies x=20-18}$

${\underline{\red{\sf{\leadsto x=2}}}}$

Therefore the required answer is .

• x =2 & y =18.
• x=18 & y =2

Answer 2

$\sf{\underline{Answer}}$

• (2,18) and (18,2)

$\sf{\underline{Concept\:Used\:}}$

• Firstly let any two unknown variable(a,b).Then put the given value to form a equation. At last solve the equation for value of a,b

$\bf{Let\:the\:numbers=a,b}$

So,

• ab = 36...........( 1 )

• a+b = 20 ...........( 2 )

From ( 2 ) we get

• a = 20 - b ...........( 3 )

Put value of a in eqn ( 1 )

$\implies\sf{(20-b)b=36}$

$\implies\sf{20b-\ b^{2}-36=0}$

$\implies\sf{\ b^{2}-20b+36=0}$

$\implies\sf{\ b^{2}-18b-2b+36=0}$

$\implies\sf{b(b-18)-2(b-18)=0}$

$\implies\sf{(b-18)(b-2)=0}$

$\sf{\purple{b=18\:,\:2}}$

From this we get the two value of b , Now put these two value of b in eqn. (3) to get value of a

$\sf a = 20 - b$ $\implies\sf{a=20-18}$= 2

$\sf a = 20 - b$ $\implies\sf{a=20-2}$= 18

$\sf{\purple{a=2\:,\:18}}$

So , the numbers are :-

$\sf{\boxed{\boxed{18,2}}}$

$\sf{\boxed{\boxed{2,18}}}$