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TMUA 2023 · Paper 2 · Question 1 of 20

TMUA 2023 Paper 2 Question 1

Algebra and functions — Surds · equations in a substitution. Try it first; the answer and a full worked solution are below.

TMUA 2023 · Paper 2Algebra and functionsSurds · equations in a substitution8 options
Given that 1√x − 6 − 1√x + 6 = 311 what is the value of x?
  1. A2√15
  2. B4√5
  3. C5√2
  4. D√58
  5. E50
  6. F58
  7. G60
  8. H80
Show the answer and worked solution
answer · H
  1. A2√15
  2. B4√5
  3. C5√2
  4. D√58
  5. E50
  6. F58
  7. G60
  8. H80
Put u = √x. Combining over a common denominator, (u+6)−(u−6)u2 − 36 = 12u2−36. Setting this equal to 311 gives u2 − 36 = 44, so u2 = 80. Since u2 = x, we get x = 80.