"We are seeking good relations with the Soviet Union. We are seeking good relations with Communist China and the interests of world peace require good relations between the Soviet Union and Communist China." -President Richard Nixon Based on the quote, President Nixon believed that

In order to end the Vietnam war.

Explanation:

President Nixon believed that good relations with china and Soviet Union will bring peace in the world. In the government of President Nixon, Vietnam war at its peak and north Vietnam backing by the China and Soviet union and President Nixon won the election on the promise that he will end the Vietnam war and bring back US soldiers. So to end this war, good relations with china and Soviet union were necessary. He also make good relations with china in order to to gain more leverage over relations with the Soviet Union.

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