Question

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

Answer 1

\[\sqrt{2z+9 }-\sqrt{z+6}=0\]

Answer 2

\[\sqrt{2z+9}=\sqrt{z+6}\]

Answer 3

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

Answer 4

hows the work?

Answer 5

Just substitute in the original equation with z=-3 to check it's the right solution!!

Answer 6

It's right by the way!! So your answer is z=-3

Answer 7

yea i checked!

Answer 8

\[\sqrt{x+8}=x-4\]

Answer 9

What do you think?

Answer 10

x-8=x-16

Answer 11

-8 -8

Answer 12

=8

Answer 13

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?

Answer 14

yess

Answer 15

you should do*

Answer 16

Ok. Do it and show me what you get.

Answer 17

\[\sqrt({x-8})^{2}=(x-4)^{2}\]

Answer 18

\[x+8=x+16\]

Answer 19

are you sure about the right hand side?

Answer 20

(x-4)^2 is what?

Answer 21

yes because 4x4=16

Answer 22

all (x-4) is raised to the power of 2. Not only the 4.. So it's like (x-4) times (x-4)

Answer 23

??

Answer 24

:)

Answer 25

Ok.. follow my steps carefully!

Answer 26

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:
\[(x-4)^2=x^2-8x+16\]

Answer 27

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?

Answer 28

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!

Answer 29

You will find that only x=8 is a solution of the equation.