To solve the equation (x2+1)2=(992+1)2(x2+1)2=(992+1)2

To solve the equation (x2+1)2=(992+1)2(x2+1)2=(992+1)2, we can take the square root of both sides. This gives us two cases to consider:

1. x2+1=992+1x2+1=992+1
2. x2+1=?(992+1)x2+1=?(992+1)

Case 1: x2+1=992+1x2+1=992+1

Subtracting 1 from both sides:

x2=992x2=992

Taking the square root:

x=99orx=?99x=99orx=?99

Case 2: x2+1=?(992+1)x2+1=?(992+1)

This simplifies to:

x2+1=?992?1x2+1=?992?1

Which implies:

x2=?992?2x2=?992?2

Since x2x2 is always non-negative, this case has no real solutions.

Conclusion

The solutions to the equation (x2+1)2=(992+1)2(x2+1)2=(992+1)2 are:

x=99andx=?99