(2x-y-3)(2x-y+3)-(2x-y-3)^2 已知a-1/2=2,求a^2+1/a^2,a^4+1/a^4的值
问题描述:
(2x-y-3)(2x-y+3)-(2x-y-3)^2 已知a-1/2=2,求a^2+1/a^2,a^4+1/a^4的值
答
(2x-y-3)(2x-y+3)-(2x-y-3)^2=(2x-y-3)[(2x-y+3)-(2x-y-3)]=(2x-y-3)(2x-y+3-2x+y+3)=6(2x-y-3)a-1/a=2?a^2+1/a^2=(a-1/a)²+2=(2)²+2=6,a^4+1/a^4=(a²+1/a²)²-2=6²-2=34.