1. The problem statement, all variables and given/known data
Suppose ##x## and ##y## are positive real numbers.If ##x < y## , then ##x^2 < y^2##.
2. Relevant equations
Assume ##x<y## with ##x,y \in ℝ^+##.This implies that ##\exists z \in ℝ^+## such that ##x+z=y##.We have ##y^2 = (x+z)^2 = x^2 + 2xz + z^2## , and this proves that if ##x < y## with ##x,y \in ℝ^+## , then ##x^2 < y^2##.
any thoughts on that one? Thank you!
Suppose ##x## and ##y## are positive real numbers.If ##x < y## , then ##x^2 < y^2##.
2. Relevant equations
Assume ##x<y## with ##x,y \in ℝ^+##.This implies that ##\exists z \in ℝ^+## such that ##x+z=y##.We have ##y^2 = (x+z)^2 = x^2 + 2xz + z^2## , and this proves that if ##x < y## with ##x,y \in ℝ^+## , then ##x^2 < y^2##.
any thoughts on that one? Thank you!
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