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

(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+(cosα)^2]^2-2(sinα*cosα)^2
=1-2m^2/16=1-1/8=7/8.
∴(sinα)^4+(cosα)^4=7/8.