Technological advances have enabled us to solve many major problems already. Thanks to technological developments, it is now possible to build houses that are more resistant to natural disasters such as earthquakes. Advances in medical technology have made many diseases obsolete and developed treatments for previous fatal conditions. Technology can only make further advances into solving problems.
Yes, it is possible for technology to solve major problems, and in fact it does this all the time. Technology has solved many medical questions and has led to the cure or treatment of many diseases. Technology has made communication much easier, and communication is often necessary to solve problems small and large.
I think that as our technology continues to improve then many of the problems in today's society will be able to be dealt with, I think that we should always continue to invest heavily into research of new technologies, the entire human race benefits when our technology progresses to the next level.
It is always possible for technology to solve major problems. It doesn't mean that it will solve all problems. For example, having a pacemaker is technology and this solves a major problem with the heart. Technology has the power to solve or create problems and will likely do both in the future.