已知sinα cosα是方程4x^2+2根号6+m的两实根 (1)求m的值 (2)sin^4α+cos^4α的值

题目

已知sinα cosα是方程4x^2+2根号6+m的两实根 (1)求m的值 (2)sin^4α+cos^4α的值

答案

(1)根据韦达定理,sinα+cosα=-√6/2,.(1)sinαcosα=m/4,.(2),(1)式两边平方,再减2*(2)式,(sinα)^2+(cosα)^2=3/2-m/2,3/2-m/2=1,m=1,(2)(sinα)^4+(cosα)^4+2(sinα)^2(cosα)^2-2(sinα)^2(cosα)^2=[(sinα)^2...