square root of 2z+9-square root of z+6=o

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square root of 2z+9-square root of z+6=o

Mathematics
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\[\sqrt{2z+9 }-\sqrt{z+6}=0\]
\[\sqrt{2z+9}=\sqrt{z+6}\]
\[\implies \sqrt{2z+9}=\sqrt{z+6} \implies 2z+9=z+6 \implies z=-3\] Plug in the equation and check!!

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Other answers:

hows the work?
Just substitute in the original equation with z=-3 to check it's the right solution!!
It's right by the way!! So your answer is z=-3
yea i checked!
\[\sqrt{x+8}=x-4\]
What do you think?
x-8=x-16
-8 -8
=8
Well. The first thing you should here is to get rid of the square root. To do so, you should square both sides. Can you do that?
yess
you should do*
Ok. Do it and show me what you get.
\[\sqrt({x-8})^{2}=(x-4)^{2}\]
\[x+8=x+16\]
are you sure about the right hand side?
(x-4)^2 is what?
yes because 4x4=16
all (x-4) is raised to the power of 2. Not only the 4.. So it's like (x-4) times (x-4)
??
:)
Ok.. follow my steps carefully!
First start by squaring both sides: \[(\sqrt{x+8})^2=(x-4)^2\] you did the left hand side, it's the same as x+8.. the right hand side is: \[(x-4)^2=x^2-8x+16\]
Now, the equation will look like: \[x+8=x^2-8x+16 \implies x^2-9x+8=0\] Do you know how to solve a quadratic equation?
Just factorize the expression x^2-9x+8 to get: \[x^2-9x+8=0 \implies (x-8)(x-1)=0 \implies x=1, x=8\] We have two values for x. Check for each one!
You will find that only x=8 is a solution of the equation.

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