Germany | Can you solve this ? | Math Olympiad Problem

[@NidalDajani]

I guess complex answers are beyond the scope of this video. Thanks for sharing.

[@dinlendiricidrtv]

Çözüm için teşekkürler ❤ güzel çözüm oldu❤

[@manifold3d]

There is a simpler solution in 5 basic steps: (x-4) (x-5) (x-6) (x-7) = 1680 Key insight: 4 left terms are symmetric around 5.5 But let's scale first to avoid factions 1) Multiply both sides by 2^4 = 16 (absorb the 2's into each left term) (2x-8) (2x-10) (2x-12) (2x-14) = 16×1680 2) Define substitution y = 2x - 11 to reveal symmetry: (y+3) (y+1) (y-1) (y-3) = 16×1680 (y²-9) (y²-1) = 16×1680 3) Define another substitution z=y²-1 z² - 8 z = 16×1680 4) Simply solve quadratic equation z = 4 ± SQ(16×1680 + 16) z = 4 ± 4 SQ(1681) = 4 ± 4 × 41 5) z must be positive real number thus z = 168 => y = 13 => x = 12

[@wes9627]

Substitute x=y+5.5 into the given equation and rearrange to (y^2-1/4)(y^2-9/4)-1680=y^4-(5/2)y^2-26871/16=0 y^2=(5/2±164/2)/2=169/4 or -159/4, y=±13/2 or ±i√159/2, and x=(11±13)/2=12 or -1 or x=(11±i√159)/2.

[@mathpro926]

Thank you for your solution

[@bidyarjitapati8c852]

T cant be taken as common it should be t×t+2 some thing is wrong

[@devyroselina6431]

Thank you so much

[@aarnokorpela294]

Maranatha JESUS