Prove the following statements. (a) For all a,b∈R,a2+b2≥2a+4b−5. (b) For all a,b,c,d∈R,(a2+b2)(c2+d2)≥(ac+bd)2. (c) For all a,b,c∈R,a2+b2+c2≥ab+bc+ca.

A real number is a number in mathematics that can be used to measure a continuous one-dimensional qu...

Resuelto Prove the following statements. (a) For all

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Pregunta: Prove the following statements. (a) For all a,b∈R,a2+b2≥2a+4b−5. (b) For all a,b,c,d∈R,(a2+b2)(c2+d2)≥(ac+bd)2. (c) For all a,b,c∈R,a2+b2+c2≥ab+bc+ca.

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Prove the following statements. (a) For all

a, b \in R, a^{2} + b^{2} \geq 2 a + 4 b - 5

. (b) For all

a, b, c, d \in R, (a^{2} + b^{2}) (c^{2} + d^{2}) \geq (a c + b d)^{2}

. (c) For all

a, b, c \in R, a^{2} + b^{2} + c^{2} \geq ab + b c + c a