Question

√2 + √3și y = √6-1 calculeaza (x²+y²-11)la puterea 100

Answer 1

$x=\sqrt2+\sqrt3 \\ y=\sqrt{6}-1 \\ (x^2+y^2-11)^{100}=[(\sqrt2+\sqrt3)^2+(\sqrt6-1)^2-11]^{100}= \\ =(2+2\sqrt6+3+6-2\sqrt6+1-11)^{100}= (12-11)^{100}=1^{100}=\boxed{1}.$