#hard precalc/algebra 2 problem

10 messages · Page 1 of 1 (latest)

weak hill
#

the question is sqrt[(√x)+3]=x-3. i've tried every method under the sun: substituting u for √x, squaring both sides twice, even taking the ln and derivatives of both sides (wrong strategy, but i was at my wit's end)

what's more is that my teacher's solution–according to themself btw–is very unintuitive. this is their solution:

I love this question but i cannot for the life of me find a way to crack it

25sRJi6R.jpg
rustic pilotBOT
dusky sigil
#

that's probably the most elegant solution

#

your method of squaring twice works too tho

#

you'd get $x = (x-3)^4 - 6(x-3)^2 + 9$

lilac capeBOT
#

Donkey

902819665317855264.png
dusky sigil
#

and after that factorize it via hit and trial

#

find 1,4 to be the integer roots

#

and quadratic formula the rest

#

beyond that its a matter of plugging the roots into your original solution to check for extraneous roots