Question

Find the two numbers whose sum is 9 and product is 20.




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Answer 1

Step-by-step explanation:

let the numbers be x and 9-x.

then,thier product=20

so,x(9-x)=20

so,the equation will be,

-x+9x-20=0.

take minus sign outside.then,it will be

-(x-9x+20)=0.

x-9x+20=0

x-4x-5x+20=0.

1(x-4)-5(x-4)=0

(x-4) (1-5) =0

then the zeros will be,

x=4 and x=-4

so, the two numbers will be

if,x=4 , (9-x)=9-4=5.

if,x=-4, (9-(-4))=9+4=13

Answer 2

Given,

The sum of the two numbers = 9

The product of the two numbers = 20

To find,

The two numbers.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the first number = x

And, The second number = y

So,

Their sum will be = (x+y)

And, their product will be = (x×y) = xy

According to the data mentioned in the question,

(x+y) = 9 ....(1)

xy = 20 ....(2)

Now,

(x+y)² = 9²

(x-y)² + 4xy = 81

(x-y)² + (4×20) = 81

(x-y)² + 80 = 81

(x-y)² = 81 - 80

(x-y)² = 1

(x-y) = ± 1 ....(3)

Adding (3) with (1), we get :

(x+y)+(x-y) = 9+1 (when x = 1)

2x = 10

x = 5

Or,

(x+y) + (x-y) = 9-1 (when x = -1)

2x = 8

x = 4

Putting the value(s) of x, in equation (2)

5 × y = 20

y = 20/5

y = 4

Or,

4 × y = 20

y = 20/4

y = 5

Thus,

Values of x and y are either 5 and 4 respectively, or , 4 and 5 respectively.

Hence, the numbers are 4 and 5