Objective 3 - Solving Radical Equations (Linear)

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Solve radical equations that lead to linear equations.

Link to section in online textbook.

First, watch this video to see how solving radical equations is different from solving linear and quadratic equations. The major difference is in the restricted domains of radical functions! This objective will focus on radical equations that lead to linear equations. That means we can have 0 or 1 solution (based on whether the potential solution is in the domains of the radical functions).

Solve the following equation. If there is no Real solution, type ”NA”.

$\sqrt {\sage {factor9A}} = \sqrt {\sage {factor9B}}$

Potential Solution: $x = \answer [tolerance=0.05]{\sage {answer9}}$

Actual Solution: $x = \answer [tolerance=0.05]{\sage {answer9}}$

How can we tell if the potential solution (the value we get from squaring both sides and solving) is an actual solution? Is there anything we need to worry about when it comes to square root functions? (think domain)

Solve the following equation. If there is no Real solution, type ”NA”.

$\sqrt {\sage {factor11A}} = \sqrt {\sage {factor11B}}$

Potential Solution: $x = \answer [tolerance=0.05]{\sage {answer11}}$

Actual Solution: $x = \answer [format=string]{NA}$

Solve the following equation. If there is no Real solution, type ”NA”.

$\sqrt {\sage {factor12A}} = \sqrt {\sage {factor12B}}$

Potential Solution: $x = \answer [tolerance=0.05]{\sage {answer12}}$

Actual Solution: $x = \answer [format=string]{NA}$

Solve the following equation. If there is no Real solution, type ”NA”.

$\sqrt {\sage {factor10A}} = \sqrt {\sage {factor10B}}$

Potential Solution: $x = \answer [tolerance=0.05]{\sage {answer10}}$

Actual Solution: $x = \answer [tolerance=0.05]{\sage {answer10}}$

Press...	...to do
left/right arrows	Move cursor
shift+left/right arrows	Select region
ctrl+a	Select all
ctrl+x/c/v	Cut/copy/paste
ctrl+z/y	Undo/redo
ctrl+left/right	Add entry to list or column to matrix
shift+ctrl+left/right	Add copy of current entry/column to to list/matrix
ctrl+up/down	Add row to matrix
shift+ctrl+up/down	Add copy of current row to matrix
ctrl+backspace	Delete current entry in list or column in matrix
ctrl+shift+backspace	Delete current row in matrix

Type...	...to get
norm	$\|\|\blue{[?]}\|\|$
text	$\text{\blue{[?]}}$
sym_name	$\backslash\texttt{\blue{[?]}}$
abs	$\left\|\blue{[?]}\right\|$
sqrt	$\sqrt{\blue{[?]}}$
paren	$\left(\blue{[?]}\right)$
floor	$\lfloor \blue{[?]} \rfloor$
factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
sub	${\blue{[?]}}_{\blue{[?]}}$
frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
deriv	$\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}$
sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
root	$\sqrt[\blue{[?]}]{\blue{[?]}}$
vec	$\left\langle \blue{[?]} \right\rangle$
mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
arcsin	$\arcsin\left(\blue{[?]}\right)$
arccos	$\arccos\left(\blue{[?]}\right)$
arctan	$\arctan\left(\blue{[?]}\right)$
sin	$\sin\left(\blue{[?]}\right)$
cos	$\cos\left(\blue{[?]}\right)$
tan	$\tan\left(\blue{[?]}\right)$
sec	$\sec\left(\blue{[?]}\right)$
csc	$\csc\left(\blue{[?]}\right)$
cot	$\cot\left(\blue{[?]}\right)$
log	$\log\left(\blue{[?]}\right)$
ln	$\ln\left(\blue{[?]}\right)$
alpha	$\alpha$
beta	$\beta$
gamma	$\gamma$
delta	$\delta$
epsilon	$\epsilon$
zeta	$\zeta$
eta	$\eta$
theta	$\theta$
iota	$\iota$
kappa	$\kappa$
lambda	$\lambda$
mu	$\mu$
nu	$\nu$
xi	$\xi$
omicron	$\omicron$
pi	$\pi$
rho	$\rho$
sigma	$\sigma$
tau	$\tau$
upsilon	$\upsilon$
phi	$\phi$
chi	$\chi$
psi	$\psi$
omega	$\omega$
Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
Sigma	$\Sigma$
Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

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