10. Solve each equation, giving your answers as simply as possible in terms of surds: a) x(x + 4) = 4(x + 8); b) x − √48 = 2√3 − 2x; c) x√18 − 4 = √8; d) x√5 + 2 = √20(x − 1).

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a) x² + 4x = 4x + 32, so x² = 32. Therefore x = ±4√2.
b) √48 = 4√3, so x − 4√3 = 2√3 − 2x. Thus 3x = 6√3, and x = 2√3.
c) √18 = 3√2 and √8 = 2√2. Hence 3√2x − 4 = 2√2, so 3√2x = 4 + 2√2. Therefore x = (2 + 2√2)/3.
d) √20 = 2√5, so x√5 + 2 = 2√5(x − 1). Rearranging gives √5x = 2 + 2√5, hence x = 2 + 2√5/5.

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