Question

14. Ifi= -1, prove the following: (x + 1 + i)(x + 1 - i)(x - 1 - i)(x - 1 + i) = x +4.

11th - 12th Class

Maths

Solution

120

4.0 (1 ratings)

As we know that ( (a+b)(a-b)=a^{2}-b^{2} ) Therefore ( ((x+1)+i)((x+1)-i)(b(-)-i)((x-1)+i) ) ( left((x+1)^{2}-i^{2}right)left((x-1)^{2}-i^{2}right) ) ( left((x+1)^{2}+1right)left((x-1)^{2}+1right) ) ( left((x+1)^{2}+1right)left((x-1)^{2}+1right) ) ( left(x^{2}+1+2 x+1right)left(x^{2}+1-2 x+1right) ) ( left(left(x^{2}+2right)+2 xright)left(left(x^{2}+2right)-2 xright) ) ( left(left(x^{2}+2right)^{2}-(2 x)^{2}right) ) ( =x^{4}+4+4 x^{2}-4 x^{2} ) ( =x^{4}+9 ) ( =R cdot H cdot S )