z.2 a + b = 1 a^2 + b^2 = 7 ------------------ Mamy ( a^2 + b^2)^2 = a^4 + b^4 + 2 *a^2* b^2 czyli a^4 + b^4 = ( a^2 + b^2)^2 - 2*(a *b)^2 ================================== oraz ( a + b)^2 = a^2 + b^2 + 2 a*b Po podstawieniu mamy 1^2 = 7 + 2 a*b ==> 2 a*b = - 6 a*b = - 3 ------------ zatem a^4 + b^4 = 7^2 -2*( - 3)^2 = 49 - 2*9 = 49 - 18 = 31 ============================================== z.1 3 x^2 - 10 x + 3 < = 0 delta = (-10)^2 - 4*3*3 = 100 - 36 = 64 p(delty) = 8 x1 = [ 10 - 8]/6 = 1/3 x2 = [ 10 + 8]/6 = 3 Ponieważ a = 3 > 0, zatem ramiona paraboli skierowane są ku górze czyli 3 x^2 - 10 x + 3 < = 0 <=> x należy do < 1/3 ; 3 > ===================================================
