Menu Close

help-x-1-1-2-x-2-1-1-3-4-find-x-

Tinku Tara 0 Comments
Pin




Question Number 62045 by hovea cw last updated on 14/Jun/19
help (x+1)^(1/2) +(x^2 −1)^(1/3) =4 find x
help(x+1)1/2+(x2−1)1/3=4findx
Answered by MJS last updated on 14/Jun/19
(x+1)^(1/2) +(x^2 −1)^(1/3) =4 (x^2 −1)^(1/3) =4−(x+1)^(1/2) both sides^3 x^2 −1=12x+76−(x+49)(√(x+1)) 77+12x−x^2 =(x+49)(√(x+1)) both sides^2 [we will get some false solutions] x^4 −25x^3 −109x^2 −651x+3528=0 trying factors if 3528 ⇒ x_1 =3 looking at the graph of f(x)=(x+1)^(1/2) +(x^2 −1)^(1/3) −4 we see it′s the only real solution if you need complex solutions you must solve (x−3)(x^3 −22x^2 −175x−1176)=0 using Cardano′s formula
(x+1)1/2+(x2−1)1/3=4(x2−1)1/3=4−(x+1)1/2bothsides3x2−1=12x+76−(x+49)x+177+12x−x2=(x+49)x+1bothsides2[wewillgetsomefalsesolutions]x4−25x3−109x2−651x+3528=0tryingfactorsif3528⇒x1=3lookingatthegraphoff(x)=(x+1)1/2+(x2−1)1/3−4weseeit′stheonlyrealsolutionifyouneedcomplexsolutionsyoumustsolve(x−3)(x3−22x2−175x−1176)=0usingCardano′sformula

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *