idontknow

  1. tahirimanov19

    Inequalities for idontknow, and for everyone else.

    1. If a, b, c are sides of the triangle, prove for any $x \in \mathbb{R}$ $$b^2x^2+(b^2+c^2-a^2)x+c^2>0$$ 2. $$(a_1b_1+a_2b_2+a_3b_3)^2 \le ({a_1}^2+{a_2}^2+{a_3}^2)({b_1}^2+{b_2}^2+{b_3}^2)$$ 3. Prove, if $a>0, \; b>0$, $$\dfrac{a+b}{1+a+b} < \dfrac{a}{1+a} + \dfrac{b}{1+b}$$ 4. If...