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The product of any two integers is a positive integer?
No, if a negative integer is multiplied by a positive integer, the product is negative. However, if both of the integers are either positive or negative, the product is positive.
Prove that if a and b are rational numbers then a plus b is a rational number?
Because a is rational, there exist integers m and n such that a=m/n. Because b is rational, there exist integers p and q such that b=p/q. Consider a+b. a+b=(m/n)+(p/q)=(mq/nq)+(pn/mq)=(mq+pn)/(nq). (mq+pn) is an integer because the product of two integers is an integer, and the sum of two integers is an integer. nq is an integer since the product of two integers is an integer. Because a+b equals the quotient of two integers, a+b is rational.
The product of three positive integers is 42 The sum of two of these integers is 9 the third integer is A1 B7 C6 D3 or E2?
D3.
Is the product of two perfect squares sometimes a perfect square?
yes..always a perfect square A perfect square is the product of an integer by itself. If you multiply a perfect square x² by another perfect square y² you get x²y² = x·x·y·y = x·y·x·y = (x·y)² which is a perfect square. Note that the product of two integers will also be an integer so x·y must be an integer because if x² and y² are perfect squares x must be an integer and y must be an integer and x·y is therefore a product of 2 integers.
The sum of two integers with different sings is 8?
Choose any integer. Let's call it "n". Then subtract 8 - n, to get the other integer. (For the two integers to have different signs, one of the integers must be greater than 8, the other will be negative.)
