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Mathematics

Solve :

x4 - 10x2 + 9 = 0

Quadratic Equations

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Answer

Let x2 = y,

⇒ x4 - 10x2 + 9 = 0

⇒ y2 - 10y + 9 = 0

⇒ y2 - 9y - y + 9 = 0

⇒ y(y - 9) - 1(y - 9) = 0

⇒ (y - 1)(y - 9) = 0

⇒ y - 1 = 0 or y - 9 = 0      [Zero product rule]

⇒ y = 1 or y = 9.

∴ x2 = 1 or x2 = 9

⇒ x = 1=±1\sqrt{1} = \pm 1 or x = 9=±3\sqrt{9} = \pm 3

Hence, x = +3, -3, +1, -1.

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