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Question
Solve the following by reducing them to quadratic equations:
z4 - 10z2 + 9 = 0.
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Solution
Given equation z4 - 10z2 + 9 = 0
Putting z2 = x, then given equation reduces to the form x2 - 10x + 9 = 0
⇒ x2 - 9x - x + 9 = 0
⇒ x(x - 9) -1(x - 9) = 0
⇒ (x - 9) (x - 1) = 0
⇒ x - 9 = 0 or x - 1 = 1
⇒ x = 9 or x = 1
But z2 = x
∴ z2 = 9
⇒ z = ±3
or
z2 = 1
z = ±1
Hence, the required roots are ±3, ±1.
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