Ask Question
23 October, 21:49

Solve by Extraneous : sqrt x+7-x=1

+4
Answers (1)
  1. 23 October, 23:50
    0
    √ (x+7) - x=1

    √ (x+7) = x+1

    [√ (x+7) ]² = (x+1) ²

    x+7=x²+2x+1

    x²+x-6=0

    x=[-1⁺₋√ (1+24) ]/2 = (-1⁺₋5) / 2

    We have two possible solutions:

    x₁ = (-1-5) / 2=-6/2=-3

    x₂ = (-1+5) / 2=4/2=2

    We must check the answer:

    if x₁=-3 ⇒√ (x+7) - x=√4 + 3=2+3=5≠1; then x₁=-3 is not a solution for this equation.

    if x₂=2; ⇒√ (x+7) - x=√9-2=3-2=1; then x₂=2 is a solution for this equation.

    answer: the only one solution is x=2;
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Solve by Extraneous : sqrt x+7-x=1 ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers