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[@SidneiMV]

Awesome! Congratulations Sir

[@RashmiRay-c1y]

We have x^3=11√(85)-32. Let y^3= 11√(85)+32. Then y^3-x^3=64 and (yx)^3=9261 = (21)^2. So, yx=21. Let t=y-x. So, 64 = t[t^2 + 63] which gives t=y-x=1 which in turn means 21/x-x=1 and so x=1/2[√(85) -1].

[@neerajgupta7856]

You r posting similar questions again and again

[@neerajgupta7856]

Root85-1/2

[@Quest3669]

8 x^3= (√85-1)^3 or
X= (√85-1)/2

[@gregevgeni1864]

.. x³ = 11√85 -32 => . ..
x = (√85 -1)/2

[@RealQinnMalloryu4]

{x^3+x^3 ➖}2048/170={x^6+2048}/170=114.10 4.2^5 4.2^1 2^2.2^1 2^1.1^1 2.1 (x ➖ 2x+1).

[@Shobhamaths]

x=(√85-1) /2👍
x^3=11√85-32
y^3=11√85+32
xy=21;
x^3-y^3=-64
x-y=-1
x^2+x-21=0
x=(√85-1) /2

[@nandeeshnagarajaiah8662]

(x^3-√1024)/√85=11
x^3=11√85+32
=(a√85-b)^3
=(a^3)85√85-b^3-3b(a^2).85+3(b^2)a√85)
=(√85)(85a^3+3ab^2)-(b^3-255ba^2)
(85a^3+3ab^2)=11
(b^3-255ba^2)=-32
(85+3)/8=11
a^3=1/8, a^2b=1/8
(1-255)/8=-32
b^3=1/8; ba^2=1/8
From the two equations
a=b=1/2
x=((1/2)√85)-(1/2)=((√85)-1)/2

[@ShriH-d1o]

x³=11√85 -32; 8x³=88√85 -256;
let 2x=a-b;
=> 8x³=(√85)³-1³ + 3√85√85(-1) +3√85(-1²)
=(√85-1)³; {=(85+3)√85 - (3)85-1
=88√85 - 256 => x³=11√85-32}; 2x=√85-1;
=> x =(√85 -1)/2