France | Can you solve this ? | Math Olympiad.

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[@learncommunolizer]

Note .X ≠ 0
Because by checking 0/0≠1 it's undefined,
Thank you all for noticing this

[@Taric25]

0/0 is not undefined. It is indeterminate. We need calculus (or a graph) to see if x = 0 is a solution. The limit of (7^x -11^x)/√(77^x-121^x) as x approaches 0 is equal to 0, so x=0 is not a solution, because 0 ≠ 1.

[@markmurto]

In this case, solved in a much simpler way. But the exercise was what it was. By observation, if x >0, the answer is complex. If x=0, we get undefined So for all real solutions x

[@tranghuynh1253]

Only x = -1.5335 is the final solution because when check x = 0, (7^x - 11^x)/(sqrt (77^x - 121^x)) is underfined

[@learncommunolizer]

Thank you

[@yvonrandriamianjaraelison6546]

Dès le début il faut préciser que le dénominateur doit être non nul donc que x soit different de zéro,par conséquent la solution x=O est à rejeter

[@cachotrelles4715]

Excelentemente explicado. Gracias

[@РусланХамеев-и6ф]

Зачем умножать обе части на (ab-b^2) до вынесения общего мнржителя b в знаменателе? В итоге (a-b)^2/b(a-b). Квадрат убирается и домножить на b вроде проще

[@markmurto]

Exactly.

[@الحمدلله-ع8ش1د]

الحل صحيح لكن نسيت خطوة تعويض الحلول في المسألة لذلك فإن x=0 ليس حلا للمسألة فتحصل على صيغة معينة وشكرا لك سيدي

[@Taric25]

The limit of (7^x -11^x)/√(77^x-121^x) as x approaches 0 is equal to 0, so 0 is not a solution in this case, because 0 ≠ 1.

[@markmurto]

Actually as x ->0, the expression goes to undefined. Not 0.

[@Taric25]

@@markmurto No, function approaches 0, as x approaches 0. If you don't believe me, graph the function or put it in Wolfram Alpha and ask it to take the limit as x approaches 0. Also, 0/0 is not undefined. It's indeterminate. Only non-zeo numbers divided by 0 are undefined.

[@indrajitkatira5953]

Here x=0 is absurd rejected

[@duanephinney300]

You either forgot to check x=0 as a viable solution or you are mistaken that 0/0 is somehow equal to 1. Please check your work.

[@learncommunolizer]

Thank you very much

[@Taric25]

There are certain cases where 0/0 can be equal to something finite. Remember, a non-zero number divided by zero is undefined, but 0/0 is indeterminate. For example, (2x)/(x) is obviously equal to 2, but in the case where x=0, we can use calculus (or a graph) to determine that as x approaches 0, (2x)/(x) still approaches 2.

[@souzasilva5471]

Zero does not serve as an answer, as it violates the condition of initial existence.

[@PavelYakovleff]

Решение неверное, садись 2.