Question

Solving radical equations

Answer 1

Answer:

• top: no solution
• bottom: x = 7

Step-by-step explanation:

I find a graphing calculator very helpful to solving radical equations. It helps avoid extraneous solutions.

top

  √(-14x +2) = x -3

  -14x +2 = x² -6x +9 . . . . . square both sides

  x² +8x +7 = 0 . . . . . . . . . .subtract the left side

Descartes' rule of signs tells you this has no positive real solutions. (There are no sign changes among the coefficients.) The value of the radical will be non-negative, so we must have x-3≥0, or x≥3. Since there are no positive real solutions to the quadratic, there are no values of x≥3 that will satisfy the equation. NO SOLUTION

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bottom

  4√(x -3) = 8 . . . . . given

  √(x -3) = 2 . . . . . . divide by 4

  x -3 = 4 . . . . . . . . . square both sides

  x = 7 . . . . . . . . . . . add 3