#Why is the positive a value removed?

39 messages · Page 1 of 1 (latest)

rocky totem
smoky canopyBOT
oak crescent
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Because when we squared both sides we've introduced another case
ie say we have
x = -5

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if we square both sides we get

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x^2 = (-5)^2

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so

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x^2=25

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if we solve that we get x = -5,5
so a new solution (x = 5) was introduced
thats why you have to be careful

rocky totem
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yes but the answer completely ommits the positive value

oak crescent
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when doing algebraic manipulations that involve even powers

rocky totem
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and only continues with the positive value

oak crescent
oak crescent
rocky totem
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oh ok i see

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then

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how am i supposed to know which value to use

oak crescent
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If we're talking about real numbers when you raise both sides to an even power you introduce a new solution as ive shown here
the fix? plug in all of your solutions at the end to see which actually works

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ie here if we plug in 2

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(the "solution" theyve ommitted)

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we get
2x2 = -sqrt(4+4)sqrt2
2x2= -sqrt8sqrt2
2x2=-sqrt16
2x2=-4
4=-4

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but if you plug in -2(our second solution)

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youll get

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2x-2 = -sqrt(4+4)sqrt2
-4=-sqrt(8)sqrt(2)

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-4=-sqrt(16)

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-4=-4

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so the solution is actually a true solution and not one we've introduced at the end

rocky totem
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i see. usually the second solutions is always telling us something

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so i assumed that it was also a valid solution

oak crescent
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Well be careful when dealing with powers and dividing both sides by a variable, you might be introducing or removing solutions without noticing

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btw while we're at it if you divide both sides by the variable check for the case where the variable equals 0 since you eliminate it when dividing both sides by it since you cant divide by 0 so youve assumed it isnt equal to 0

rocky totem
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yea

oak crescent
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Ik this seems unrelated but its the same idea of introducing/removing solutions during the solving process

rocky totem
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^^

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okie thanks

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.solved

smoky canopyBOT
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Solved

Post marked as solved by @rocky totem.

Use .unsolved if this was a mistake.

oak crescent
rocky totem