For natural numbers a and b, $(a+b)^2- (a - b)^2>29$ and the smallest value of ab is m. The value of $(m^2+m+1)$ is

73

$(a+b)^2- (a - b)^2>29$

a² + b² + 2ab - a² - b² + 2ab > 29

4ab > 29

If 4ab is greater then 29 then it must be the multiple of 4 more than 29

So we can take the value of 4ab = 32

then, ab = 8 = m

Now, $(m^2+m+1)$ = $(8^2+8+1)$ = 73