已知x^-2+x^2=2×2^1/2,且x＞1,則x^2-x^-2的值為 A.-2或2 B.-2 C.6^1/2 D2

熱心網友

x^2+x^(-2)=2√2---x^4-2√2x^2+1=0---x^2=√2+'-1 x1---x^21 & √2-1x^2=√2+1---x^2-x^(-2)=x^2-1/x^2=(√2+1)-1/(√2+1)=(√2+1)-(√2-1)=2

熱心網友

A設 t=x^2-x^-2所以 t^2=(x^2-x^-2)^2 =(x^2+x^-2)^2-4 =(2√2)^2-4 =8-4 =4 t=-2或2