# An algebra problem by mridul jain

Algebra Level 5

Find $$a_{}^{}x^5 + b_{}y^5$$ if the real numbers $$a_{}^{}$$, $$b_{}^{}$$, $$x_{}^{}$$, and $$y_{}^{}$$ satisfy the equations \begin{align} ax + by &= 3^{}_{}\\ ax^2 + by^2 &= 7^{}_{}\\ ax^3 + by^3 &= 16^{}_{}\\ ax^4 + by^4 &= 42^{}_{}. \end{align}

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