\(\overline{ab}+\overline{ba}=100\)

\(\Rightarrow10a+b+10b+a=100\)

\(\Rightarrow11a+11b=100\)

\(\Rightarrow11\left(a+b\right)=100\)

\(\Rightarrow a+b=\dfrac{100}{11}\)

But x \(\in N\)* and \(y\in N\)

=> Don't have a,b satisfactory 

We have :

ab + ba = 100

<=> 2.a.b = 100

<=> ab = 50

So ab = 50

We have :

ab + ba = 100

<=> 2.a.b = 100

<=> ab = 50

So ab = 50

ab+¯¯¯¯¯ba=100

⇒10a+b+10b+a=100

⇒11a+11b=100

⇒11(a+b)=100

⇒a+b=10011

But x ∈N

* and y∈N

=> Don't have a,b satisfactory

We have:

 ab + ab = 100

<=> ab = 50

So , ab = 50

ab + ba = 100

<=> 2.a.b = 100

<=> ab = 50

So ab = 50

ab + ba = 100

<=> 2.a.b = 100

<=> ab = 50

So ab = 50