Question

the factor form of z²+1/z²+2-2z-2/z is
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Answer 1

Step-by-step explanation:

z²+1/z²+2=(z+1/z)²

-2z+21/z=-2(z+1/z)

Ans = (z+1/z)(z+1/z-2).

Answer 2

Answer:

(z + $\frac{1}{z}$ - 2) (z + $\frac{1}{z}$)

Step-by-step explanation:

[FIRST SQUARE (z + $\frac{1}{z}$) USING IDENTITY ]

(z + $\frac{1}{z}$)² = z² + $\frac{1}{z^{2} }$ + 2

[NOW (- 2z - $\frac{2}{z}$) IS MISSING, SO ADD THEM BOTH THE SIDES]

⇒ (z + $\frac{1}{z}$) × (z + $\frac{1}{z}$) - 2z - $\frac{2}{z}$ =  z² + $\frac{1}{z^{2} }$ + 2 - 2z - $\frac{2}{z}$

⇒ (z + $\frac{1}{z}$) × (z + $\frac{1}{z}$) - 2(z + $\frac{1}{z}$) = z² + $\frac{1}{z^{2} }$ + 2 - 2z - $\frac{2}{z}$

[ HERE z + $\frac{1}{z}$ AND - 2 ARE COMMON]

⇒ (z + $\frac{1}{z}$ - 2) (z + $\frac{1}{z}$) = z² + $\frac{1}{z^{2} }$ + 2 - 2z - $\frac{2}{z}$

HENCE FACTORS OF  z² + $\frac{1}{z^{2} }$ + 2 - 2z - $\frac{2}{z}$ ARE ⇒

(z + $\frac{1}{z}$ - 2) (z + $\frac{1}{z}$)

THANK YOU