Japanese | Can You Solve? | A Nice Olympiad Mathematics |

[@jorgecoelho4615]

thank you Mr. I really thank you

[@에스피-z2g]

x and y are two roots of the equation of t^2-12t+12=0 t=6+2rt6, 6-2rt6 (x,y)=(6+2rt6,6-2rt6), (6-2rt6,6+2rt6)

[@Misha-g3b]

(6+2V6, 6-2V6), (6-2V6, 6+2V6).

[@rashel1]

thanks

[@ApexGC91732]

x+y=12 square both sides (x+y)²=12 x²+2xy+y²=12² given xy=12 x²+2(12)+y²=12² x²+24+y²=12² x²+y²=144-24=120 x²+y²=120 x²=120-y² x=√(120-y²)= √120-y x=√4×30-y x=2√30-y now xy=12 (2√30-y)y=12 (2√30)-y²=12 (2√30)²-y⁴=144 (2√30+y²)(2√30-y²)=144 root 1 2√30+y²=144 y²=144-2√30 y=√(144+2√30) y=12+√(2√30) now x=2√30-y x=2√30-(12+√(2√30) x=2√30-12+(√(2√30)

[@rashel1]

thanks

[@ApexGC91732]

@rashel1 welcome, by the way I'm only in 8th grade

[@dominicfox1358]

@@ApexGC91732 I thought Einstein was dead

[@ASINGH-li8eq]

You explained it in easy and slowly in understandable way. Respect ! Respect Redpect !

[@ApexGC91732]

@@ASINGH-li8eq 🗿

[@rachidkada2483]

X^2-sX+p=0. s=x1+x2. .p=x1.x2...