1.

Xpower4 +4xcube +6xsquare +4x+9 if x=-1+√-2

Answer»

ANSWER:

{x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4x + 9

x = - 1 + \sqrt{2} i

x + 1 = \sqrt{2} i

(x + 1) {}^{2} = ( \sqrt{2} i) {}^{2}

{x}^{2} + 2x + 1 = 2 {i}^{2} = - 2

{x}^{2} + 2x + 3 = 0

SQUARING both SIDES, we GET

( {x}^{2} + 2x + 3) {}^{2} = 0

{x}^{4} + 4 {x}^{2} + 9 + 4 {x}^{ 3} + 12x + 6 {x}^{2} = 0

{x}^{4} + 4 {x}^{3} + 10 {x}^{2} + 12x + 9 = 0


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