Math

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1. √x-10+4=0
Answer: x=26

2.√3x+1=7
Answer: x=16

Help With These:

3. √x+6=x
how would you solve this?
I don't get how would It?

4. √x+4 = √x-1+1

it looks similar to problem 2 but it doesn't quite have the same amount of numbers in the same spots..
So I'm stuck on how to solve it.

  • Math -

    √(x-10) + 4 = 0
    if x=26, you have
    √16 + 4 = 0
    which is not true.
    √n is a positive value, so there is no solution.
    Now, √(x-10) - 4 = 0 has solution x=26

    √(3x+1) = 7
    has the solution x=16 as you say.

    √(x+6) = x
    square both sides:
    x+6 = x^2
    now solve as a quadratic
    x = -2 or 3
    However, √4 = 2, not -2, so -2 is an extraneous solution introduced by squaring. -2+6 = 4 = (-2)^2, but √4 = 2, not -2.

    same method here:

    x+4 = (x-1) + 2√(x-1) + 1
    4 = 2√(x-1)
    16 = 4(x-1)
    x = 5
    check: √(5+4) = √9 = 3 = √(5-1)+1 OK

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