Working With A Nice Radical Expression
VloĆŸit
- Äas pĆidĂĄn 8. 07. 2024
- đ€© Hello everyone, I'm very excited to bring you a new channel (SyberMath Shorts).
Enjoy...and thank you for your support!!! đ§Ąđ„°đđ„łđ§Ą
/ @sybermath
/ @aplusbi
â Join this channel to get access to perks:â bit.ly/3cBgfR1
My merch â teespring.com/stores/sybermat...
Follow me â / sybermath
Subscribe â czcams.com/users/SyberMath?sub...
â Suggest â forms.gle/A5bGhTyZqYw937W58
If you need to post a picture of your solution or idea:
intent/tweet?text...
#algebra #radicals #radicalequations
via @CZcams @Apple @Desmos @NotabilityApp @googledocs @canva
PLAYLISTS đ” :
ⶠTrigonometry: ⹠Trigonometry
ⶠAlgebra: ⹠Algebra
ⶠComplex Numbers: ⹠Complex Numbers
ⶠCalculus: ⹠Calculus
ⶠGeometry: ⹠Geometry
ⶠSequences And Series: ⹠Sequences And Series
Another way would be just calling y = sqrt(x). This gives us the equation yâŽ-18yÂČ-17y=0. By inspection, we quickly notice that y=-1 is a possibility. So, by Briot-Ruffini, we have yÂł-yÂČ-17y=0, or y(yÂČ-y-17)=0, and therefore, y=0 or y=(1±sqrt(69))/2. Returning to x, as we have y = sqrt(x), the only admissible values are those who are â„0. So sqrt(x) can be 0 (and then, x=0, and therefore, x-sqrt(x)=0) or (1+sqrt(69))/2 (and then, x=(35+sqrt(69))/2, and therefore, x-sqrt(x)=17).
Zero is asnwer too.
Method 2 slightly quicker if you factor out sqrt(x)+1 sooner.
An edit on second method
xÂČ-x=17(x+sqrx)
(x-sqrx)(x+sqrx)=17(x+sqrx)
(x-sqrx)=17
xÂČ - 18x = 17âx => (xÂČ - x) - (17x + 17âx) = 0
aÂČ - bÂČ = (a-b)(a+b)
If
a = x,
b = âx
then
(xÂČ - x) = (x - âx)(x + âx)
and
(x - âx)(x + âx) - 17(x + âx) = 0
or
(x + âx)*(x - âx - 17) = 0
Therefore
1) x + âx = 0 => x = 0 and x - âx = 0
2) x - âx = 17
17
Let A=x-âx; A*(x+âx) = x^2 - x; Eqn: x^2 - x = 17(x+âx); A*(x+âx) =17( 17(x+âx); A = 17
xÂČ - 18x = 17âx
find E = x - âx
âx⎠- 18âxÂČ = 17âx
âx(âxÂł - 18âx - 17) = 0
âx = 0 => x = 0 => *E = 0*
âxÂł - 18âx - 17 = 0
âxÂł + 1 - 18âx - 18 = 0
(âx + 1)(âxÂČ - âx + 1) - 18(âx + 1) = 0
âxÂČ - âx - 17 = 0 => *E = x - âx = 17*