Math Olympiad | A Nice Algebra Problem

[@user-kp2rd5qv8g]

Let a = sort(5/24) and b= 1/2(1/sqrt(2) - 1/sqrt(3)). The the expression to be evaluated is N=(a+b)^4 + (a-b)^4 = 2[(a^2+b^2)^2 +4a^2 b^2. (a^2+b^2)^2 = 31/144 -(5 sqrt(6))/72 and 4a^2b^2=25/144- (5sqrt(6))/72. Thus, N = 1/18[14 -5 sqrt(6)].

[@kassuskassus6263]

(56 - 11sqrt(6)) / 72

[@RajeshKumar-wu7ox]

(199-80√6)/288

[@user-ny6jf9is3t]

(14-5×ριζα6)/18

[@RealQinnMalloryu4]

(20/96+{(1)^2/*8)^2 ➖ (1)^2/(12)^4 }= {1/64 ➖ 1/244} ={0+0 ➖}/180.=1/180 {20/96+1/180}=21/276 =10.66 2^5.6^11 2^1.6^11^1 2^1.61^1 2^1.3^2^1^1 1^1.3^2 3^2 (x ➖ 3x+2). (1)^2/(24)^4 = 1/1152{ 1+1 ➖/8+8 ➖ +1+1 ➖/12+12 ➖} =4/40 {1/1152 ➖ 4/40} =3/1112 =37.2 37^1.2^1 1^1 .2^1 2^1(x ➖ 2x+1)

[@RajeshKumar-wu7ox]

0.0105584