Question

докажи неравенство (x-5)^2+3x>7(1-x)

Answer 1

$(x-5)^2+3x textgreater 7(1-x) \x^2-10x+25+3x textgreater 7-7x \x^2+25 textgreater 7 \x^2 textgreater -18$
x^2 всегда больше или равно 0, следовательно:
$x^2textgreater -18, forall x in R Rightarrow (x-5)^2+3x textgreater 7(1-x), forall x in R$