To prove that an integer k such that 4k + 3 is a perfect square does not exist, we can show that there is no integer k that satisfies this condition.
A perfect square is a number that can be expressed as the product of two equal integers. For example, 4 is a perfect square because it can be written as 2 x 2.
If we plug in some integer values for k and see what happens, we can quickly see that 4k + 3 can never be a perfect square. For example, if we let k = 1, then 4k + 3 = 7, which is not a perfect square. If we let k = 2, then 4k + 3 = 11, which is also not a perfect square.
We can continue this process for any integer value of k and we will always end up with a number that is not a perfect square. Therefore, we can conclude that there does not exist an integer k such that 4k + 3 is a perfect square.
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Answer:
To prove that an integer k such that 4k + 3 is a perfect square does not exist, we can show that there is no integer k that satisfies this condition.
A perfect square is a number that can be expressed as the product of two equal integers. For example, 4 is a perfect square because it can be written as 2 x 2.
If we plug in some integer values for k and see what happens, we can quickly see that 4k + 3 can never be a perfect square. For example, if we let k = 1, then 4k + 3 = 7, which is not a perfect square. If we let k = 2, then 4k + 3 = 11, which is also not a perfect square.
We can continue this process for any integer value of k and we will always end up with a number that is not a perfect square. Therefore, we can conclude that there does not exist an integer k such that 4k + 3 is a perfect square.
Step-by-step explanation: