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Question
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
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Solution
Given x4 - 26x2 + 25 = 0
Putting x2 = y, the given equation reduces to the form y2 - 26y + 25 = 0
⇒ y2 - 25y - y + 25 = 0
⇒ y(y - 25) -1(y- 25) = 0
⇒ (y - 25) (y - 1) = 0
⇒ y - 25 = 0 or y - 1 = 0
⇒ y = 25 or y = 1
∴ x2 = 25
⇒ x = ± 5
or
x2 = 1
x = ±1
Hence, the required roots are ±5, ±1.
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