Prove that if n is an odd integer, then n +4n - 2 is also odd....

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Prove that if n is an odd integer, then n³ +4n² - 2 is also odd. Prove that if æ and y are rational numbers, and x + y 0, then is rational. Hint: you may need to use the fact that if a fraction is nonzero, then its numerator must be nonzero. We say that an integer n is a perfect cube if we can write n= k³ for some positive integer k. (a) Use the definition to show that 343 is a perfect cube. (b) Prove that the product of any two perfect cubes is always a perfect cube. Prove that if n is an odd integer, then n³ +4n² - 2 is also odd. Prove that if æ and y are rational numbers, and x + y 0, then is rational. Hint: you may need to use the fact that if a fraction is nonzero, then its numerator must be nonzero. We say that an integer n is a perfect cube if we can write n= k³ for some positive integer k. (a) Use the definition to show that 343 is a perfect cube. (b) Prove that the product of any two perfect cubes is always a perfect cube.