Ukraine l Very Nice Olympiad Math Radical Problem l m=?

[@NadirMemon-hk7ki]

❤❤❤❤

[@BrijLalSahu-bb1lu]

Very nice @MATHS TUTORIAL (BL SAHU)

[@wes9627]

Thinking outside the box, 49-9=40. 7^{√m/2}=7^2, so √m/2=2 or √m=4 or m=16.
Check: 7^{√16/2}=7^{4/2}=49, 3^{√16/2}=3^{4/2}=9, and 49-9=40

[@jonathancapps1103]

If m is an integer, u = (√m)/2, and x = 7^(u/2), must x be an integer? Maybe I just need caffeine, but that's the only step I can't follow.

[@Krauzer33]

Same question here, i don't understand that restriction. Also why in 11=7^(u/2) solution impossible? If you can not calculate it in your head, that doesn't mean that you can't calculate it at all

[@nasrullahhusnan2289]

Note that 40=49-9
=7²+3²
=[sqrt(7)]⁴-[sqrt(3)]⁴
It is clear that m=16

[@novellobrancher9627]

👏👏👏and..happy good year!

[@haiderlughmani]

Thank you.💝

[@АндрейАнцышкин]

😊m=4 моментально

[@ghlscitel6714]

M=16