<s>[INST] If $a_1,a_2,a_3$ are roots $x^3+7x^2-8x+3,$ find the polynomial with roots $a_1^2,a_2^2,a_3^2$ If $a_1,a_2,a_3$ are the roots of the cubic $x^3+7x^2-8x +3,$ find the cubic polynomial whose roots are:
$a_1^2,a_2^2,a_3^2$ and the polynomial whose roots are $\frac{1}{a_1}, \frac{1}{a_2}, \frac{1}{a_3}.$ Not really sure where to go. Hints appreciated. 
 [/INST] HINT:
For the first let $y=x^2$
$\implies x^2(x+7)=8x-3\implies y=x^2=\dfrac{8x-3}{x+7}$
Express $x$ in terms of $y$ and put the value of $x$ in the given cubic equation and simplify.
For the second, let $z=\dfrac1x\implies x=\dfrac1z$
and put the value of $x$ in the given cubic equation  and simplify.
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