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# Help with error? watch

1. Where is the error in this ...

(x+5)^(1/2)=x+3

x+5=x^2+6x+9

x^2+5x+4=0

(x+4)(x+1)=0

hence x=-4 or x=-1
2. (Original post by Econowizard)
Where is the error in this ...

(x+5)^(1/2)=x+3

x+5=x^2+6x+9

x^2+5x+4=0

(x+4)(x+1)=0

hence x=-4 or x=-1
Check that both solutions work in the original equation. When you square both sides of an equation, you will often generate extra solutions. E.g.

has one solution

has two solutions.

For most algebraic manipulation from step 1 to step 2, step 1 implies step 2 and step 2 implies step 1. For example, adding 2 to both sides of an equation.

But in cases such as squaring, this isn't true so the final solutions that you get many not satisfy the original equation.
3. if you sketch the graphs of y = ( x + 5 ).5 and y = x + 3 you can see they only intersect once.
4. (Original post by Econowizard)
Where is the error in this ...

(x+5)^(1/2)=x+3

x+5=x^2+6x+9

x^2+5x+4=0

(x+4)(x+1)=0

hence x=-4 or x=-1
I'd solve this slightly differently:

Let

(for real solutions)

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