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Question Number 200657 by cherokeesay last updated on 21/Nov/23

Answered by Frix last updated on 21/Nov/23

3((27x^2 +24x+((28)/3)))^(1/4) =4+((((81x)/2)−1))^(1/3) 3(((81x^2 +72x+28)/3))^(1/4) =4+(((81x−2)/2))^(1/3) x=(t/9) 3(((t^2 +8t+28)/3))^(1/4) =4+(((9t−2)/2))^(1/3) Now I′m looking for both roots to vanish. Starting with ((9t−2)/2)=n^3 ⇔ 9t=2(n^3 +1). Very obviously t=n=2 is a solution. 3(((2^2 +8×2+28)/3))^(1/4) =4+(((9×2−2)/2))^(1/3) 3(((48)/3))^(1/4) =4+(((16)/2))^(1/3) 3×((16))^(1/4) =4+(8)^(1/3) 3×2=4+2 True ⇒ x=(2/9)

327x2+24x+2834=4+81x2−13381x2+72x+2834=4+81x−223x=t93t2+8t+2834=4+9t−223NowI′mlookingforbothrootstovanish.Startingwith9t−22=n3⇔9t=2(n3+1).Veryobviouslyt=n=2isasolution.322+8×2+2834=4+9×2−22334834=4+16233×164=4+833×2=4+2True⇒x=29

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