Question
Find the value of (2-\sqrt{5} )^{198}\cdot (9+4\sqrt{5} )^{99}
Find the value of (2-\sqrt{5} )^{198}\cdot (9+4\sqrt{5} )^{99}
(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