Quadratic in negative or reciprocal fractional powers

Solve equations where the variable appears with negative or reciprocal exponents (e.g. 1/x², 1/x⁴, x^(1/3), x^(2/3)) that form a quadratic structure upon substitution.

4 questions · Moderate -0.1

1.02f Solve quadratic equations: including in a function of unknown

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CAIE P1 2007 June Q4

4 marks Standard +0.3

4 Find the real roots of the equation \(\frac { 18 } { x ^ { 4 } } + \frac { 1 } { x ^ { 2 } } = 4\).

OCR C1 2009 January Q3

5 marks Standard +0.3

3 Solve the equation \(3 x ^ { \frac { 2 } { 3 } } + x ^ { \frac { 1 } { 3 } } - 2 = 0\).

OCR C1 2012 January Q5

5 marks Moderate -0.3

5 Find the real roots of the equation \(\frac { 3 } { y ^ { 4 } } - \frac { 10 } { y ^ { 2 } } - 8 = 0\).

Edexcel AS Paper 1 2019 June Q2

8 marks Moderate -0.8

Find, using algebra, all real solutions to the equation
1. \(16 a ^ { 2 } = 2 \sqrt { a }\)
2. \(b ^ { 4 } + 7 b ^ { 2 } - 18 = 0\)