√(√A + B)

E

evanr1234

New member
Joined
Jan 31, 2019
Messages
13
Hi Everyone,

I don't understand why if we have

√ ( x + 3 ) = √ x + 1

and we square both sides to obtain:

x + 3 = √(√x + 1)

we get

x + 3 = x + 2 √ x + 1. <- this is the step I don't understand)

In my mind if we take √(√x + 1) we can't really do anything with that because √ (A + B) dose NOT equal √ A + √ B

Thanks for your time!
 
evanr1234 said:
Hi Everyone,

I don't understand why if we have

√ ( x + 3 ) = √ x + 1

and we square both sides to obtain:

x + 3 = √(√x + 1).........................Incorrect

we get

x + 3 = x + 2 √ x + 1. <- this is the step I don't understand)

In my mind if we take √(√x + 1) we can't really do anything with that because √ (A + B) dose NOT equal √ A + √ B

Thanks for your time!
Click to expand...
√ ( x + 3 ) = √ x + 1

and we square both sides to obtain:

x + 3 = √(√x + 1) .........................Incorrect

It should be:

√ ( x + 3 ) = √ x + 1 and we square both sides to obtain:

[√ ( x + 3 )]2 = [√ x + 1]2

[√ ( x + 3 )] * [√ ( x + 3 )] = [√ x + 1] * [√ x + 1]

(x + 3) = √ x * √ x + √ x * 1 + 1 * √ x + 1 *1

x + 3 = x + 2 * √ x + 1 ......................................................edited (hope Jomo is asleep now)

continue......
 
Last edited by a moderator:
evanr1234 said:
I don't understand why if we have √ ( x + 3 ) = √ x + 1
and we square both sides to obtain: x + 3 = √(√x + 1)
Click to expand...
If \(\displaystyle \sqrt{x+3}=\sqrt{x}+1\\x+3=x+2\sqrt x+1\\2=2\sqrt x\\1=\sqrt x\\1=x\)
What is your question?
 
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