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The equation which can be reduced to the quadratic form; where \( x \neq 0 \) is: a) \( x-\frac{1}{x}=1 \), b) \( x^{2}+\frac{1}{x}=1 \) c) \( x^{2}+2 \sqrt{x}-1=0 \) d) \( (\sqrt{x})^{2}-2^{2}=0 \) |
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Answer» Correct option is (a) x - 1/x = 1 (a) x - 1/x = 1 ⇒ x2 - 1 = x ⇒ x2 - x - 1 = 0 which is a quadratic equation. (b) x2 + 1/x = 1 ⇒ x3 + 1 = x ⇒ x3 - x + 1 = 0 which is a cubic equation (c) x2 + 2√x - 1 = 0 ⇒ x2 - 1 = -2√x ⇒ (x2 - 1)2 = 4x ⇒ x4 - 2x2 + 1 = 4x ⇒ x4 - 2x2 - 4x + 1 = 0 which is a quartic equation (d) (√x)2 - 22 = 0 ⇒ x - 4 = 0 which is a linear equation. |
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