Problem 3.3 (MATH 461 only) Let x, y be in X and a E R. Prove...

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Problem 3.3 (MATH 461 only) Let x, y be in X and a E R. Prove that ||ax + (1 a)y|| + a(1 a)||x y|| = a||x|| + (1 a)||y||. Hint: Recall that ||u + v|| = ||u|| + ||v|| + 2 (u, v). Problem 3.3 (MATH 461 only) Let x, y be in X and a E R. Prove that ||ax + (1 a)y|| + a(1 a)||x y|| = a||x|| + (1 a)||y||. Hint: Recall that ||u + v|| = ||u|| + ||v|| + 2 (u, v).