Starting with (n + 5) / sqrt(n - 1) = k and so n + 5 = sqrt(n - 1) k we square both sides and get: n² + 10n -k²n +k² = -25 (n- k² + 11) (n - 1) = -36 (k² - n - 11) (n - 1) = 36 So to divide 36 by (n - 1) n must be 2, 3, 4, 5, 7, 10, 13, 19 or 37. But k² must also be a perfect square, so only n = 2 (k² = 49), n =5 (k² = 25), n = 10 (k² = 25) and n = 37 (k² = 49) solves the equation.
![[Full Episode] The Restaurant War Thailand ศึกพ่อค้าซ่าแม่ค้าแซ่บ Episode 4 | 13 ต.ค. 67](http://i.ytimg.com/vi/h8N9tY46P-M/mqdefault.jpg)
Alternatively, you may start with p^2 = n-1, then it will lead to the same but slightly easier solution.🤩
Nice, yes this is essentially the same, but saves the awkwardness of writing sqrt(n-1) a bunch of times
Nice video
Starting with (n + 5) / sqrt(n - 1) = k and so n + 5 = sqrt(n - 1) k we square both sides and get:
n² + 10n -k²n +k² = -25
(n- k² + 11) (n - 1) = -36
(k² - n - 11) (n - 1) = 36
So to divide 36 by (n - 1) n must be 2, 3, 4, 5, 7, 10, 13, 19 or 37. But k² must also be a perfect square, so only n = 2 (k² = 49), n =5 (k² = 25), n = 10 (k² = 25) and n = 37 (k² = 49) solves the equation.
Nice solution!
0:29 a rational number? Man ... *rolling eyes*
I could see at a glance that n must be 1 + a perfect square, also called a square number.
Much more interesting would be: find all n element R that lead to the quotient being element N.
Yep. The answer is
2n = m²-20±m√(m²-24)
for all integer m, m≥5. Right?
My Euler, writing n+5 as √(n-1)√(n-1)+6? Is this some kind of joke ... ?
The Indian fellas have a specific way of abstraction
Nice ❤
@@JOSHUVASRINATH gracias!
Only one of those n values produces an integer for the initial expression, the rest produce rationals, if my mental arithmetic is working this morning
@@TypoKnig I don't think your mental arithmetic was working this morning 😂😅
@@JPiMaths You’re right - I was wrong. No more math before my caffeine kicks in!
@@TypoKnig 😂😂😂