Solving Equations with Radicals: X = 3 + sqrt(X2 - 9)

[lokilenox]

the current problem is

X = 3 + sqrt(X2 - 9)

i'm not sure how to do this problem. i have taken pages of notes on this subject, but no matter how many times i scroll through it, i can't seem to find ANYTHING over squared variables within a square root... i did a problem previously, but the # came out evenly....

it was

sqrt(x2 + 4) - sqrt(X + 10) = 0 i worked it out, and came out with the answer as 4, i havn't been graded yet, so i don't know for sure if it was right or not, but i believe so. i know how to do these problems, but i can't seem to work this one out, and i'm doing it on the computer... any help would be appriciated.... plz?

 

[Denis]

Re: help! i'm Solving Equations with Radicals!! totally lost!

X = 3 + sqrt(X2 - 9)

Show x squared this way: x^2

x = 3 + sqrt(x^2 - 9)
x - 3 = sqrt(x^2 - 9) : square both sides:
x^2 - 6x + 9 = x^2 - 9 : rule: [sqrt(n)]^2 = n

OK? Finish it.

 

[stapel]

i'm not sure how to do this problem. i have taken pages of notes on this subject, but...i can't seem to find ANYTHING over squared variables within a square root.

To learn how to solve radical equations, please consider studying some of the many great lessons available online. :idea:

. . . . .Google results for "solving radical equations"

Note: To learn how to format mathematics online, please review the lessons at the links you saw in the "Read Before Posting" thread you read before posting. Or, if you prefer, you can learn how to do LaTeX formatting by following the links in the "Forum Help" pull-down menu at the very top of every forum page. :wink:

Have fun!

Eliz.

 

[lokilenox]

Re: help! i'm Solving Equations with Radicals!! totally lost!

Show x squared this way: x^2

x = 3 + sqrt(x^2 - 9)
x - 3 = sqrt(x^2 - 9) : square both sides:
x^2 - 6x + 9 = x^2 - 9 : rule: [sqrt(n)]^2 = n

OK? Finish it.

Oh, *slaps self in head* i can't believe i forgot that! stupid ADHD, i always try to rush through the problems, without watching too carefully... now i feel really stupid... thanks! i knew it had to be something STUPID that i was overlooking! :roll: oh well, at least i'll remember it now!


THANKS A BUNDLE!!!

 

[Deleted member 4993]

\(\displaystyle \sqrt{x^2+4}\, - \sqrt{x+10} = 0\)

\(\displaystyle \sqrt{x^2+4}\, = \sqrt{x+10}\)

\(\displaystyle x^2+4\, = \,x+10\)

\(\displaystyle x^2 - x - 6\, = \,0\)

\(\displaystyle (x + 2)(x - 3)\, = \,0\)

\(\displaystyle x = \,-2\,,or \,3\)