An EASY Way to Crack Radical Math Problem | Algebra Challenge

[@Quest3669]

Finally ..X^4= 24√5+ (56)= or
X^2= 6+2√5 or x= √5+(1) soln.

[@潘博宇-k4l]

E=10+4(6)^(1/2)

[@Fjfurufjdfjd]

(5)^(1/2)+1

[@RealQinnMalloryu4]

{x^4+x^4 ➖ }+{80+80 ➖}+{48+48 ➖ }={x^8+160+96},256x^8 x^3 2 ➖ x^2 (21)^2 ➖ (40)^2/25 256x^8 x^3 2 ➖ x^2 {441 ➖ 160}=/25=25x^8 x^3 2 ➖{ x^2* 311}/25=256x^8 x^3 2 ➖ 311x^2/25=256x^8 x^3 (2)^2 ➖ 12.11x^2=256x^8 {x^3 *4} ➖ 12.11x^2=256x^8{ 4x^3 ➖ 12.11x^2}={256x^8 +12.7x^1}=14.63x^9 14.30^33x^9 14.30^11x^9 14.15^15^11x^9 4.5^5^5^6x^3^6 4^.2^3^2^3^2^3x^3^2^3 2^2^ 1^1^1^1^1^1x1^1^3 1^2.x^1^3 2x^3 (x ➖ 3x+2).

[@ManojkantSamal]

*=read as square root
Ans:: *5+1......May be
Explain matter

[@ManojkantSamal]

^=read as to the power
*=read as square root
Let's explain the part
{21-(40/*5)}
=(21.*5 -40)/*5
=*5(21.*5 -40)/(*5.*5)
=(105-40.*5)/5
={80+25-(40.*5)}/5
={(4.*5)^2+(5^2)-(2×4.*5×5)}/5
=(4.*5 -5)^2/(*5^2)
={(4.*5-5)/*5}^2
=[{*5(4-*5)}/*5]^2
=(4-*5)^2
So,*{(4-*5)^2}=4-*5
Now,
2-(4-*5)=2-4+*5
=*5-2
=8(*5-2)/8
=(8.*5 - 16)/8
={(5.*5)+(3.*5)-1-15}/8
=[(*5)^3-(1^3)-{3×(*5)^2).1}+{3×*5×(1^2)}]/8
=(*5-1)^3/(2^3)
={(*5-1)/2}^3
So,
[{(*5-1)/2}^3]^(1/3)
=(*5-1)/2
So,
48×{(*5-1)/2}
(48.*5 -48)/2
So,
80+{(48.*5 -48)/2}
{160+(48.*5)-48}/2
=(112 +48.*5)/2
=2(56+24.*5)/2
=56+24.*5
=36+20 +(24.*5)
=(6^2)+(2.*5)^2 + {2×6×(2.*5)}
=(6+2.*5)^2......
={(*5)^+(1^2)+(2×1×*5)}^4
={(*5+1)^2}^2
=(*5+1)^4
As per question
{(*5+1)^4}^(1/4)
=*5+1
Hence the solution is (*5 +1)

[@gregevgeni1864]

1 + √5 .
Because
21 - 40/√5 = 21 - (40√5)/(√5)² =
= 21 - (40√5)/5 = 21 - 8√5 =
21 - 2•4√5 = 4²-2•4√5+ √5² =
=(4-√5)² => √(21-40/√5)= 4-√5 (1).
³√(2- √21-40/√5))= ³√(2-(4-√5))=
= ³√(-2+√5) = ³√((-16+8√5)/8)=
=³√((√5³-3√5²•1+3√5•1²-1³)/8)=
= ³√((√5-1)³/2³)= (√5-1)/2 .
⁴√(80+48(√5-1)/2)= ⁴√(80+24√5-24)=⁴√(56+24√5)=
⁴√(36+2•6•2√5+√5²)=⁴√(6+2√5)²=
√(6+2√5) = √(√5²+2•1•√5+1²)=
√(√5+1)²=√5+1.