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Question-183711




Question Number 183711 by Michaelfaraday last updated on 29/Dec/22
Commented by Matica last updated on 29/Dec/22
to mathematize
tomathematize
Answered by HeferH last updated on 29/Dec/22
 ((x^2 ((x^2 ((x^2 ...))^(1/3) ))^(1/3) ))^(1/3)  = H   ((x^2 H))^(1/3)  = H   Hx^2 =H^3    x = H  (√(x^2  + x(√(x^2  + x(√(x^2  + x(√(...)))))))) = P   (√(x^2  + x∙P)) = P   x^2  + Px = P^2    x^2  + Px − P^2  = 0   (x/P) + 1 − (P/x) = 0   let (x/P) = t   t + 1 − (1/t) = 0   t^2  + t − 1 = 0   t = ((−1 ±(√(1 − 4(1)(−1))))/(2(1))) = ((−1±(√5))/2)    (x/P) = ((−1 + (√5))/2)   ((2x)/( (√5) −1)) = P  ⇒    (x/((2x)/( (√5) − 1))) = (x/5) ⇒ ((2x)/( (√5) − 1)) = 5   x = ((5(√5) − 5)/2)
x2x2x2333=Hx2H3=HHx2=H3x=Hx2+xx2+xx2+x=Px2+xP=Px2+Px=P2x2+PxP2=0xP+1Px=0letxP=tt+11t=0t2+t1=0t=1±14(1)(1)2(1)=1±52xP=1+522x51=Px2x51=x52x51=5x=5552
Commented by JDamian last updated on 29/Dec/22
In this step   x^2 +Px=P^2   why don′t you solve quickly as a quadratic  equation? You have changed into another  quadratic equation in t and solved to get P,  which is unnecessary.
Inthisstepx2+Px=P2whydontyousolvequicklyasaquadraticequation?YouhavechangedintoanotherquadraticequationintandsolvedtogetP,whichisunnecessary.
Commented by Michaelfaraday last updated on 29/Dec/22
thanks sir  but sir i think you should have solve it  inform of quadratic eqn from  x^2 +px−p^2 =0 while your solving from eqn  which is not necessary.
thankssirbutsirithinkyoushouldhavesolveitinformofquadraticeqnfromx2+pxp2=0whileyoursolvingfromeqnwhichisnotnecessary.
Commented by HeferH last updated on 29/Dec/22
 Yeah you are right , in my defense    it was very late (00:48) when i did it
Yeahyouareright,inmydefenseitwasverylate(00:48)whenididit
Commented by Michaelfaraday last updated on 29/Dec/22
okay sir
okaysir

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