linear equations

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Given: square root of 5 minus x is equals to x plus 1. Show that the solution to the above equation lies in the interval of negative 1less than or equals to x less than or equals to 5. Solve the equation. Solve the equation negative square root of 5 minus x is equals to x plus one

  • linear equations -

    √(5-x) = x+1

    To be defined, 5-x ≥ 0
    -x ≥ -5
    x ≤ 5
    also since √anything yields a positive result, x+1≥0
    x≥-1
    so -1 ≤ x ≤ 5

    To solve, square both sides
    5-x = x^2 + 2x + 1
    x^2 + 3x - 4 = 0
    (x+4)(x-1) = 0
    x = -4 or x = 1
    because of our domain, x = 1

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