Germany | Math Olympiad | A Nice Algebra Problem👇

[@arvindkulkarni6580]

LOVELY SOLUTION MAAM

[@harikishan1900]

Explanation is very helpful 👌

[@aruntiwari5714]

It's very good explained here

[@satyadev3848]

perfect solution here

[@harshpathak2359]

Nice 👍

[@KeshavKulkarni-x1w]

Very nice 👍

[@manojchaugule794]

good explaination

[@Maheshkumar-cw6un]

Very well done

[@RealQinnMalloryu4]

{4x^2+6x^2}/9x^2=10x^4/9x^2= 1.1x^2=1^1.1^1x^2 1x^2 (x ➖ 2x+1).

[@vdarasun]

When multiple on x-3, you need mark x#3.

[@Nikioko]

x² + [3x / (x − 3)]² = 16
x² + 9x² / (x² − 6x + 9) = 16
9x² / (x² − 6x + 9) = 16 - x²
9x² = (16 − x²) (x² − 6x + 9)
9x² = 16x² − 96x + 144 − x⁴ + 6x³ − 9x²
x⁴ − 6x³ + 2x² + 96x − 144 = 0

[@SidneiMV]

x - 3 = u => x = u + 3
(u + 3)² + 3²(u + 3)²/u² = 16
(u + 3)²(1 + 9/u²) = 16
(u² + 6u + 9)(1 + 9/u²) = 16
u² + 6u + 9 + 9 + 54/u + 81/u² - 16 = 0
u² + 81/u² + 6u + 54/u + 2 = 0
(u² + 81/u²) + 6(u + 9/u) + 2 = 0
u + 9/u = t
t² = u² + 81/u² + 18
u² + 81/u² = t² - 18
t² - 18 + 6t + 2 = 0
t² + 6t - 16 = 0
(t + 8)(t - 2) = 0
t = -8
u + 9/u = -8
u² + 8u + 9 = 0
u = (-8 ± 2√7)/2
u = -4 ± √7 => *x = -1 ± √7*
t = 2
u + 9/u = 2
u² - 2u + 9 = 0
u = (2 ± i4√2)/2
u = 1 ± i2√2 => *x = 4 ± i2√2*

[@ressouguerrier6043]

X²+(3x|x-3)²=16, Resolvons l'equation: (x²-6x+9)x²+3x²|x²-6x+9=16:x⁴-6x³+9x²+3x²|x²-6x+9=16: Reduisons les termes semblabes,x⁴-6x³+12x²|x²-6x+9=16:x⁴-6x³+12x²=16(x²-6x+9): x⁴-6x³+12x=16x²-96x+144:x⁴-6x³+12x²-16x²+96x-144=0:x⁴-6x³-4x²+96x-144=0; x⁴-6x³-4x²+96x =144:x(x³-6x²-4x+96)=144:x=144, x³-6x²-4x+96=0: x³-6x²-4x=-96; x(x²-6x-4)=-96; x=-96:x²-6x+4=0: ∆=b²-4ac:,∆=(-6)²-4×1×4; ∆=36-16=>,∆=20;∆=√2²×5: ∆=2√5; x'=-b+√∆|2a: x'=6+2√5|2: x'=2(3+√5)|2: x'=3+√5: x"=-b-√∆|2a: x"=6-2√5|2; x"=2(3-√5)|2: x"=3-√5;

[@Power9500]

it Was 10|2 and suddenly in the next column 10 🫥 she forgot to transfer the right digits 😂