Germany l can you solve this?? l Nice biquadratic equation.

Germany l can you solve this?? l Nice biquadratic equation.
Olympiad Mathematics l Olympiad problem l Easy solution l Olympiad preparation l Easy Solution l Very Tricky Solution l Olympiad Test Preparation.
#mathsolympiad #maths #mathcompetition #mathcontest #mathstricks #education #biquadraticequation #equation #solution #mathmastertv

[@НеллиПшено]

Решаем методом устного счета.
х-12=0
х=12.
х-14=0
х=14.
Good luck!

[@sy8146]

Thank you for explaining. I solved by letting s=x-13.
Then, the given equation is (s+1)^4+(s-1)^4=16. ∴ 2s^4+12s^2+2=16 ∴ s^4+6s^2-7=0 ∴ (s^2+7)(s^2-1)=0 ∴ s = ±1, ±(√7)i
∴ x = s+13 = 12, 14, 13±(√7)i [ I guess this way is a little easier for calculating. ]

[@hadithsharif-qj3nj]

Sir ap logics bari kamal ki lagate split karr karr ke

[@haiderlughmani]

Thank you.

[@tunneloflight]

trivial. For non-complex solutions: It is obvious that when x = 12 or 14, one part goes to zero, while the other equals 16. Done. x = {12,14}

[@prollysine]

letu=x-12 , u^4-4u^3+12u^2-16u=0 , u(u^3-4u^2+12u-16)=0 , u=0 , x=12 , u^3-4u^2+12u-16=0 , (u-2)(u^2-2u+8)=0 , u=2 , x=14 ,
u^2-2u+8=0 , u=(2+/-V(4-32))/2 , u= 1+/-i*V7 , x= 13+i*V7 , 13-i*V7 , solu , x= 12 , 14 , 13+i*V7 , 13-i*V7 ,

[@silvaadamyan9098]

Let t=x-13, (t+1)^4 + (t-1)^4=16, t^4+4t^3+6t^2+4t+1+ t^4-4t^3+6t^2-4t+1=16, 2t^4+12t^2+2=16, t^4+6t^2+1=8, let m= t^2, m^2+6m-7=0, m^2+7m-m -7=0, m(m+7)-(m+7)=0, (m+7)(m-1)=0, m=1 m=-7 (not satisfied, no real solutions, as m=t^2).t^2=1, t=+/-1, x-13=1 x=14 and x-13=-1 x=12.