An algebra problem by mridul jain

Algebra Level 5

Find ax5+by5a_{}^{}x^5 + b_{}y^5 if the real numbers aa_{}^{}, bb_{}^{}, xx_{}^{}, and yy_{}^{} satisfy the equations ax+by=3ax2+by2=7ax3+by3=16ax4+by4=42.\begin{aligned} ax + by &= 3^{}_{}\\ ax^2 + by^2 &= 7^{}_{}\\ ax^3 + by^3 &= 16^{}_{}\\ ax^4 + by^4 &= 42^{}_{}. \end{aligned}

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