Math Interview Tricks: From Stanford, Harvard, Cambridge to Oxford University

[@E.h.a.b]

Log(x)^4 - 16 Log(x) = 12 Let x = 10^y, we get y^4 - 16 y - 12 = 0 --> [0] Split the fourth degree equation into two quadratic equations y^4 - 16 y - 12 = (y^2 + a y + b)(y^2 + d y + e) Compare the coefficients of y on both sides y^3 : a+d = 0 --> d = -a --> [1] y^2 : a.d+e+b = 0 --> e+b=a^2 --> [2] y^1 : e.a+b.d = -16 --> e-b=-16/a --> [3] y^0 : b.e = -12 --> [4] From [4] we know that b.e are combinations of (1*12, 2*6, 3*4) so I will check the correct values ​​of them in [1] and [2] From [2] we find that e+b for all combinations (1*12, 3*4) will not give a real perfect square, so I neglect them and I need to only check (2, 6) (2, -6) --> a^2 = 2-6 = -4 is rejected (-2, 6) --> a^2 = -2+6= 4 --> a = +/- 2 From [2] -2-6=-16/a --> a = 2, so we get a=2, d =-2, e=-2, b=6 and our equation will be: (y^2 + 2 y + 6)(y^2 - 2 y - 2) = 0 (y^2 + 2 y + 6)= 0 has no real solution, so we only have (y^2 - 2 y - 2)= 0 y =(2+/-√(4-4(1)(-2)))/2 =(1 +/- √3) After checking the validity of [y] in equation [0] we get that (1 +/- √3) are valid roots. x = 10^(1+√3), 10^(1-√3) ----> [Answer]

[@superacademy247]

Thanks for sharing your perspective with everyone ✅💪✅💕💯

[@justekiara1953]

Thank-u, teacher

[@superacademy247]

You're welcome! Glad you found the video helpful 👍.

[@НеллиПшено]

Решаем методом устного счета. Сокращаем уравнение на 4. lg x-4lg x=3 -3lg x=3 x=10^-1 Good luck!

[@rob876]

let log x = u u^4 - 16u - 12 = 0 (u^2 + 2u + 6)(u^2 - 2u - 2) = 0 u = 1 - √3, 1 + √3 x = 10^(1-√3), 10^(1+√3)