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<ol class="abc-list"><li><div class="list-item-paragraph">If $x$ and $y$ are positive integers and $x\ne y$, prove that $xy\left( x+y \right)&lt;{{x}^{3}}+{{y}^{3}}$.</div></li><li><div class="list-item-paragraph">If $a$, $b$, $c$ and $d$ are real numbers such that $a+b+c+d=1$, prove that ${{a}^{2}}+{{b}^{2}}+{{c}^{2}}+{{d}^{2}}\ge \frac{1}{4}$.<br><br></div></li></ol>

Proving Elementary Inequalities

IP3U2 HOT PN1 Q7

Linear Equations and Inequalities

<p>For two positive numbers $a$ and $b$, where $a < b$, show that $\frac{a}{b}<\frac{a+1}{b+1}$.</p>

For two positive numbers $a$ and $b$, where $a < b$, show that $\frac{a}{b}<\frac{a+1}{b+1}$.

Comparing Rational Expressions

<p>For any positive integers $m$ and $n$, show that $\frac{m}{n}+\frac{n}{m}\ge 2$.</p>

For any positive integers $m$ and $n$, show that $\frac{m}{n}+\frac{n}{m}\ge 2$.

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