Menu Close

solve-x-x-2-x-3-

Tinku Tara 0 Comments
Pin




Question Number 205680 by mnjuly1970 last updated on 27/Mar/24
solve ⌊x ⌋ + ⌊ x^2 ⌋ = ⌊ x^3 ⌋
solve⌊x⌋+⌊x2⌋=⌊x3⌋
Answered by Frix last updated on 27/Mar/24
Obviously x=0 −1<x<0: ⌊x^3 ⌋=⌊x⌋=−1∧⌊x^2 ⌋=0 0<x<1: ⌊x^3 ⌋=⌊x^2 ⌋=⌊x⌋=0 ⇒ −1<x<1 ★ x=2^(1/3) : ⌊x^3 ⌋=2∧⌊x^2 ⌋=⌊x⌋=1 The change is at x=2^(1/2) : ⌊x^2 ⌋=2 ⇒ 2^(1/3) ≤x<2^(1/2) ★ x=3^(1/3) : ⌊x^3 ⌋=3∧⌊x^2 ⌋=2∧⌊x⌋=1 The change is at x=4^(1/3) : ⌊x^3 ⌋=4 ⇒ 3^(1/3) ≤x<4^(1/3) ★
Obviouslyx=0−1<x<0:⌊x3⌋=⌊x⌋=−1∧⌊x2⌋=00<x<1:⌊x3⌋=⌊x2⌋=⌊x⌋=0⇒−1<x<1★x=213:⌊x3⌋=2∧⌊x2⌋=⌊x⌋=1Thechangeisatx=212:⌊x2⌋=2⇒213⩽x<212★x=313:⌊x3⌋=3∧⌊x2⌋=2∧⌊x⌋=1Thechangeisatx=413:⌊x3⌋=4⇒313⩽x<413★

Pin

Leave a Reply

Your email address will not be published.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