Answer

(2-\sqrt{5} )^{198}\cdot (9+4\sqrt{5} )^{99}

=(2-\sqrt{5} )^{198}\cdot [2^2+4\sqrt{5}+(\sqrt{5} )^2 ] ^{99}

=(2-\sqrt{5} )^{198}\cdot [(2 +\sqrt{5} )^2 ] ^{99}

=(2-\sqrt{5} )^{198}\cdot (2 +\sqrt{5} ) ^{198}

=[(2-\sqrt{5} )(2+\sqrt{5} )] ^{198}

=[2^2-(\sqrt{5} )^2]^{198}

=(4-5)^{198}

=1

Steven Zheng posted 1 hour ago

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