Hungary | A Nice Algebra Problem | Math Olympiad

[@anatoliyklimenko7797]

It is one liner. Original equation easily transforms to X^(X^(1/2) -3/2)=1 that has 2 solutions: 1) X = 1 and 2) X=(3/2)^2 = 9/4 (X^2-3/2 =0 ==> X=(3/2^2) = 9/4)

[@SALogics]

Very nice! ❤

[@giulio00010001]

Good lesson

[@SALogics]

Thanks! 😃

[@SALogics]

Thanks! 😃

[@فیروزاهنگری]

✓x=b , x=b^2 , (b^2)^(b^3)=(b^3)^(b^2) haw 2 case case one b^3 =b^2. ,b>0 ,b=1 , x=1 case 2 are opposite now taking ln 2b^3lnb=3b^2lnb. , 3b^2=2b^3. , b=3/2. x=9/4

[@SALogics]

Very nice! ❤

[@huangsteven6470]

Condition: x > 0 Easy to see that 1 is a result. Why dont use the logarit function, it will be better and easier way to find 9/4 as the other result.

[@SALogics]

Very nice! ❤

[@Mariosergio61]

Taking ln on both sides, the solutions (1 and 9/4) are more easily obtained. I think.

[@SALogics]

Very nice! ❤

[@jorgepinonesjauch8023]

Faltan 2 posibles soluciones mas x=1 y x=0 y hay que probarlas...??

[@SALogics]

Very nice! ❤

[@musicsubicandcebu1774]

x = 1

[@SALogics]

Yes, you are right! ❤ but what about other solutiion!