Since α , β , γ and σ are the roots of the given equation.

Therefore

x 4 + 4x 3 – 6x 2 + 7x – 9 = (x – α ) (x – β ) (x – γ ) (x – σ )

Putting x = i and then x = –i, we get

1 – 4i + 6 + 7i – 9 = (i – α ) (i – β ) (i – γ ) (i – σ )

and 1 + 4i + 6 – 7i – 9 = (–i – α ) (–i – β ) (–i – γ ) (–i – σ )

Multiplying these two, we get

(–2 + 3i) (–2 – 3i) = (1 + α 2 ) (1 + β 2 ) (1 + γ 2 ) (1 + σ 2 )

⇒ 13 = (1 + α 2 ) (1 + β 2 ) (1 + γ 2 ) (1 + σ 2 ).

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