Find the value of $a^2+b^2$, when $a+b=9$ and $ab=20$

Find the value of $p^2+q^2$, if $p-q=6$ and $p+q=14$

Find the value of $mn$, if $m+n=8$ and $m-n=2$

Find the value of $x^2+\frac{1}{x^2}$ and $x^4+\frac{1}{x^4}$ if $x+\frac{1}{x}=3$.

Find the value of $x-\frac{1}{x}$ and $x^2-\frac{1}{x^2}$, if $x+\frac{1}{x}=\sqrt{5}$

Find the value of $8x^3+84x^{2}y+294x{y}^2+343y^3$. If $x=1$ and $y=2$.