Let S= ^2 2 : ( ^4 + ^4 ) x^2+( 2 ) x+ ( ^6 + ^6 )=0 . has real roots . If and be the smallest and largest elements of the set S , respectively, then 3 (( -2)^2+( -1)^2 ) equals _________

Step-by-step solution

aligned & D=( 2 )^2-4 (1- ^2 2 2 ) (1- 3 4 ^2 2 ) & =( 2 )^2-4 (1- 5 4 ^2 2 + 3 8 ^4 2 ) & D=- 3 2 ^4 2 +6 ^2 2 -4>0 & 3 ^4 2 -12 ^2 2 +8 < 0 & ^2 2 = 12 12^2-12.8 6 = 12 4 3 6 = 6 2 3 3 & ^2 2 =2 2 3 , but ^2 2 [0,1] & =2- 2 3 , =1 ( -2)^2= 4 3 ,( -1)^2=0 & 3( -2)^2+( -1)^2=4 aligned