Asked by Junior
Can someone help me solve this type of equation.
[SQRT(x + 3)] - [SQRT(x - 2)] =1
. Also. My teacher tells me I keep getting it wrong because after I square both sides, I am supposed to foil the "lefthand side of the equation". IF anyone knows what I am talking about and can help me, I would really appreciate it.
[SQRT(x + 3)] - [SQRT(x - 2)] =1
. Also. My teacher tells me I keep getting it wrong because after I square both sides, I am supposed to foil the "lefthand side of the equation". IF anyone knows what I am talking about and can help me, I would really appreciate it.
Answers
Answered by
drwls
If you square the left side of the equation (and the right also), you get
x + 3 - 2 sqrt[(x-2)(x+3)] + x-2 = 1
That is where the "FOIL" is done, but you still have more to do. Combine terms and you get
2x - 2 sqrt[(x-2)(x+3)] = 0
Divide both sides by two, move the
-sqrt[(x-2)(x+3)] to the right side, and square both sides again.
x^2 = (x-2)(x+3)] = x^2 + x -6
Cancel out the x^2 terms
x - 6 = 0
x = 6
Plug it into your first equation and verify that it is a solution. it is
x + 3 - 2 sqrt[(x-2)(x+3)] + x-2 = 1
That is where the "FOIL" is done, but you still have more to do. Combine terms and you get
2x - 2 sqrt[(x-2)(x+3)] = 0
Divide both sides by two, move the
-sqrt[(x-2)(x+3)] to the right side, and square both sides again.
x^2 = (x-2)(x+3)] = x^2 + x -6
Cancel out the x^2 terms
x - 6 = 0
x = 6
Plug it into your first equation and verify that it is a solution. it is
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