What is the solution to y - 8y^(1/2) + 11 = 0 using quadratic formula?

[DeanBH]

first part of the question is simple :
x^2 - 8x + 11 = 0

solve. using quadratic formula it is 4 +/- root5

second part confuses me, you are given to equation:

y - 8y^(1/2) + 11 = 0

and are told to :

solve this giving answer in form p +/- Q * root5

i have no idea how to do this. the quadratic formula doesn't work on this one and i don't understand how part 1 of this question helps me with this part, can someone explain it to me please.!? thanks

 

[cristo]

Hint: Can you express y in terms of x, such that your second equation becomes your first?

 

[DeanBH]

i don't know how to do that, I've tryed making the equations equal to each other but it doesn't work out right

 

[Borek]

Compare the equations term by term.

11=11

next is...

 

[DeanBH]

oh yeah, i can do that because they're both 0, and are of the same form. lewl

 

[tiny-tim]

i don't know how to do that, I've tryed making the equations equal to each other but it doesn't work out right

Hint: substitution.

 

[DeanBH]

Hint: substitution.

i've honastly tried for ages, i still don't know how to do it.

can someone just run me through it. it's not even a question for homework or anything I am just revising and i don't understand this.

 

[tiny-tim]

Bigger hint: substitute y = x².

 

[DeanBH]

Bigger hint: substitute y = x².

why can i just substitute that.

 

[tiny-tim]

why can i just substitute that.

eh? You can substitute anything you like.

Some substitutions make the problem easier :!) , some substitutions make it harder.

But all substitutions are valid.

Try it … put y = x² into y - 8√y + 11 = 0, and see what happens!

 

[Dr Zoidburg]

why can i just substitute that.

think about it a second:
you've already found that x^{2} - 8x + 11
Now you need to find y - 8y^{1/2} + 11
If you substituted x^{2} = y,
you would have x^{2} - 8x + 11
which you already have the answer to. If x = 4+/-\sqrt{5},
what is x^{2} (i.e. y) going to equal?