For some a , b , let f(x)= | array ccc a + x x & 1 & ~b a & 1+ x x & ~b a & 1 & ~b + x x array |, x 0, _ x 0 f(x)= + a + b . Then ( + + )^2 is equal to :

Step-by-step solution

_ x 0 | array ccc a+ x x & 1 & b a & 1+ x x & b a & 1 & b+ x x array |= + a+v b At x 0 , aligned & f(x)= | array ccc a+1 & 1 & b a & 1+1 & b a & 1 & b+1 array |= + a+v b & R₁ R₁-R₂ & R₂ R₂-R₃ & | array ccc 1 & -1 & 0 0 & 1 & -1 a & 1 & b+1 array |= + a+v b & C ₂ C ₁- C ₂ & | array ccc 1 & 0 & 0 0 & 1 & -1 a & a+1 & b+1 array |= + a+v b & a+b+2= + a+v b & =2, =1, v=1 & ( + +v)=(2+1+1)^2=16 aligned