Solve the equation x¹ᐟ³ - x¹ᐟ⁶ = 2.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

1. [M1] Solves or factorises x^(1/3) - x^(1/6) - 2 = 0 oe: (x^(1/6)+1)(x^(1/6)-2)
2. [A1] x^(1/6) = 2
3. [A1] x = 64
4. [B1] Rejects x^(1/6) = -1 or x = 1 ignored at some stage, soi
5. [B1] x+2y=1
6. [M1] Dep on B1; Correctly eliminates one unknown
7. [A1] Correct quadratic in solvable form: y - 4y² [= 0] oe or 2x²-3x+1[=0] oe
8. [M1] Dep on previous M1; Factorises or solves their quadratic to get two solutions
9. [A1] y = 0, x = 1
10. [A1] y = 1/4, x = 1/2