Question: 4.5. Prove that (a+b)2 2a2+2b2 for any real numbers a and b by considering (a+ b)2+(ab)2. Similarly prove (a+b+c)2 3a2+3b2+3c2 for any real

4.5. Prove that (a+b)2 ≤ 2a2+2b2 for any real numbers a and b by considering (a+

b)2+(a−b)2. Similarly prove (a+b+c)2 ≤ 3a2+3b2+3c2 for any real a,

b, and c.

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