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If $$y^2 = y + 7$$, then what is the value of $$y^3$$?
$$y^2=y+7.$$
or, $$y^3=y\left(y+7\right).$$
or, $$y^3=\left(y^2+7y\right).$$
Now, given that $$y^2=y+7.$$,
So, $$y^3=y+7+7y.$$
or, $$y^3=7+8y.$$
A is correct choice.
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