Let us consider the one-digit number be a and the three-digit number be b.
Given that their Sum is equal to 731.
⇒ [tex]a+b=731[/tex] …(1)
Also. their product is equal to 2908.
⇒ [tex]a * b=2908[/tex] …(2)
Now, from equation (1) the value of b is
[tex]b=731-a[/tex] …(3)
Putting the value of b in equation (2), we get
⇒ [tex]a * (731-a)=2908[/tex]
⇒ [tex]731a -a^{2} =2908[/tex]
⇒ [tex]a^{2}-731a+2908 =0[/tex]
Using middle-term splitting, the equation can be written as
⇒ [tex]a^{2}-727a-4a+2908 =0[/tex]
⇒ [tex]a(a}-727)-4(a-727) =0[/tex]
⇒ [tex]a-4=0[/tex] and [tex]a-727=0[/tex]
⇒ [tex]a=4[/tex] and [tex]a=727[/tex]
Now, putting the values of a in equation (3), we get
⇒ [tex]b=731-4[/tex] and [tex]b=731-727[/tex]
⇒ [tex]b=727[/tex] and [tex]b=4[/tex]
∴ The one-digit number is 4 and the three-digit number is 727.
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