Question

根号2加1和的x次方加上根号2减1差的x次方等于6,求x

Answer 1

(√2+1)^x+(√2-1)^x=6因为√2-1=1/(√2+1)所以令a=(√2+1)^x,则(√2-1)^x=1/a所以a+1/a=6a^2-6a+1=0a=3±2√2=(√2±1)^2所以(√2+1)^x=(√2+1)^2,或(√2+1)^x=(√2-1)^2=1/(√2+1)^2=(√2+1)^(-2)所以x=2,x=-2...