Engineering Board Exam Reviewer · Quadratic Equations · hard

Find the sum of all real solutions of sqrt(2x-1)-sqrt(x-1)=1.

  1. 5
  2. 6
  3. 1
  4. 7

Answer

B. 6

Solution

Write sqrt(2x-1)=1+sqrt(x-1) and square: 2x-1=1+2sqrt(x-1)+x-1 x-1=2sqrt(x-1). Then sqrt(x-1)≤ft(sqrt(x-1)-2 )=0, so x=1 or x=5. Both satisfy the original equation, so the sum is 6.

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