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(d) Suppose a, b, c, and d are all positive integers. If ab > cd, then a + b >c+d. (e) The sum of two perfect squares is always a perfect square. (An integer is a perfect square if it is the square of another integer. For example, 25 is a perect square since it equals 5².) (f) The sum of two perfect squares is never a perfect square.

(d) Suppose a, b, c, and d are all positive integers. If ab > cd, then a + b >c+d. (e) The sum of two perfect squares is always a perfect square. (An integer is a perfect square if it is the square of another integer. For example, 25 is a perect square since it equals 5².) (f) The sum of two perfect squares is never a perfect square.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(d) Suppose a, b, c, and d are all positive integers. If ab > cd, then a + b>c+d. (e) The sum of two perfect squares is always a perfect square. (An integer is a perfect square if it is the square of another integer. For example, 25 is a perect square since it equals 5².) (f) The sum of two perfect squares is never a perfect square.
Transcribed Image Text:(d) Suppose a, b, c, and d are all positive integers. If ab > cd, then a + b>c+d. (e) The sum of two perfect squares is always a perfect square. (An integer is a perfect square if it is the square of another integer. For example, 25 is a perect square since it equals 5².) (f) The sum of two perfect squares is never a perfect square.
Prove or disprove each of the following statements. Some statements are true, but some are false. For each one, either provide a proof to verify the statement is true, or find a counterexample to establish that the claim is false.
Transcribed Image Text:Prove or disprove each of the following statements. Some statements are true, but some are false. For each one, either provide a proof to verify the statement is true, or find a counterexample to establish that the claim is false.
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