Question

零指数幂和负整指数幂已知:2x^2-3x+2=0,求x^2+x^-2的值2x的平方减3x加2等于0,求x的平方加x的-2

Answer 1

2x^2-3x+2=0,2x^2+2=3x,x^2+1=3x/2

x^2+x^-2

=x^2+1/x^2

=(x^4+1)/x^2

=[(x^2+1)^2-2x^2]/x^2

=[(3x/2)^2-2x^2]/x^2

=[(1/4)x^2]/x^2

=1/4