Let M and m respectively be the maximum and the minimum values of (f(x)= | array ccc 1+ ^2 x & ^2 x & 4 4 x ^2 x & 1+ ^2 x & 4 4 x ^2 x & ^2 x & 1+4 4 x array |, x R ) Then (M^4-m^4 ) is equal to :

Step-by-step solution

aligned & | array ccc 1+ ^2 x & ^2 x & 4 4 x ^2 x & 1+ ^2 x & 4 4 x ^2 x & ^2 x & 1+4 4 x array |, x R & R₂ R₂-R₁ & R₃ R₃ R₁ & f(x) | array ccc 1+ ^2 x & ^2 x & 4 4 x -1 & 1 & 0 -1 & 0 & 1 array | aligned Expand about R ₁ , use get f(x)=2+4 4 x M = max value of f ( x )=6m= value of f(x)=-2 m ^4- M ^4=1280