President Xi Jinping and his wife, Peng Liyuan, and US President Donald Trump and his wife, Melania Trump, pose for a photo in front of the Hall of Supreme Harmony during their visit to the Palace Museum, or the Forbidden City, in Beijing on Wednesday. LAN HONGGUANG / XINHUA

There was no reason for it not to be.

Although the differences that had been pestering bilateral ties have not instantly disappeared, the most important takeaway from their talks in Beijing has been the constructive approach to these issues the two leaders demonstrated.

Both expressed their willingness to work with, instead of against, the other in dealing with the differences between their two countries, in particular over trade and the Democratic People's Republic of Korea's nuclear program.

Beijing and Washington have been working hard to find convergences on these two prominent issues, in particular, and will very likely work harder given the two leaders' agreement that cooperation between the two countries is the "only correct choice".

But these matters are complicated and they are unlikely to have come up with any quick fixes. Although both clearly believe the issues are solvable, with Trump saying they will work together to solve not only their mutual problems but also world "problems of great danger and security", and President Xi Jinping saying China is committed to working with the United States on issues of international concern, as well as controlling the differences between the two sides.

Such precious progress in trying to find common ground, along with the Chinese commitment to establish a constructive "new-type of relationship" with the US, as Xi again elaborated in his talks with Trump, will go a long way to anchoring the all-important, yet sometimes volatile, Sino-US relationship.

The concordant note struck by Xi and Trump showcased not only the personal rapport they have established, but also consolidated optimism about the prospects for bilateral ties, especially since Xi has previously emphasized the "leading role of head-of-state diplomacy", and Trump on Thursday touted the "chemistry" between himself and his host.

There is undoubtedly a lot of work left to do, as the US secretary of state pointed out. But the readiness of the two leaders to listen, as well as talk, was apparent in their public appearances, and offers hope that together, China and the US can do "tremendous things" to the benefit of both countries, even the world, as Trump suggested.

Certainly, China is willing since, as Xi said, the Pacific is big enough to accommodate both and although there are challenges the two nations need to face, these are limited, and there is boundless potential for growth.