If a,b (a≠b), are the real roots of the equation (k + 1)(x2 + x + 1)2 + (k - 1)(x4 + x2 + 1) = 0, k ≠ 1, 0.
Then the product of the roots is
Since the equation (x2 + x + 1) = 0 . oes not have any real roots, the roots of the original equation will be the root of the equation (kx2 + x + k) = 0
Hence product of the roots = k/k = 1
Polar form of a complex number is
|z1 + z2 | =
|z1 + z2|= .
|z1| + |z2|= .
We have to prove that
Square both sides.
Square both sides again.
2x1x2y1y2 ≦ x12y22 + y12x22 and we get
0 ≦ (y1x2 - x1y2)2.
It is true because x1, x2, y1, y2 are all real.
|z1 - z2 | =
A2 + b2