The two Integers are [tex]10,10.[/tex]
What is Integer ?
An Integer number that can be written without a fractional component.
We have,
Sum of two Integers [tex]=20[/tex]
Product of two Integers [tex]=100[/tex]
Now,
Let,
One integer [tex]=x[/tex]
Another integer [tex]=y[/tex]
So,
According to the question,
[tex]x+y= 20[/tex] [tex].....(i)[/tex]
[tex]x*y=100[/tex]
⇒ [tex]x=\frac{100}{y}[/tex] [tex].....(ii)[/tex]
Now,
Putting value of x in equation (i),
We get,
[tex]\frac{100}{y}+y= 20[/tex]
[tex]100+y^2=20y[/tex]
[tex]y^2-20y+100=0[/tex]
Using middle term split method,
[tex]y^2-10y-10y+100=0[/tex]
[tex]y(y-10)-10(y-10)=0[/tex]
[tex](y-10) (y-10)=0[/tex]
We get,
[tex](y-10)=0[/tex] and [tex](y-10)=0[/tex]
So, [tex]y=10[/tex]
Now, putting value of y in in equation (i),
[tex]x+10=20[/tex]
[tex]x=10[/tex]
So, two integers are [tex]10,10.[/tex]
Hence, we can say that the two Integers are [tex]10,10.[/tex]
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