Solving 'Stanford' University Entrance Exam | Best Trick Ever!!! | a=?

[@jossamkamchanda9290]

Brilliant... beautiful...

[@MathswithChinwendu]

Thank you so much sir

[@naveenarumugam8268]

There is a simple way mam take 4 root on both sides it is completed

[@MathswithChinwendu]

Thank you

[@stpat7614]

(a - 4)^4 = 16
(a - 4)^(2 * 2) = 4^2
([a - 4]^2)^2 = (2^2)^2
Let x = (a - 4)^2, and y = 2^2
([a - 4]^2)^2 = (2^2)^2
=> x^2 = y^2
=> x^2 - y^2 = y^2 - y^2
=> x^2 - y^2 = 0
=> (x - y)(x + y) = 0
=> ([a - 4]^2 - [2^2])([a - 4]^2 + [2^2]) = 0
Let x = a - 4, and y = 2
([a - 4]^2 - [2^2])([a - 4]^2 + [2^2]) = 0
=> (x^2 - y^2)(x^2 + y^2) = 0
=> (x - y)(x + y)(x - y * i)(x + y * i) = 0
=> ([a - 4] - 2)([a - 4] + 2)([a - 4] - 2 * i)([a - 4] + 2 * i) = 0
=> (a + [- 4 - 2])(a + [- 4 + 2])(a - 4 - 2 * i)(a - 4 + 2 * i) = 0
=> (a - 6)(a - 2)(a - 4 - 2 * i)(a - 4 + 2 * i) = 0
=> a - 6 = 0, or a - 2 = 0, or a - 4 - 2 * i = 0, or a - 4 + 2 * i = 0
a1 = 6
a2 = 2
a3 = 4 + 2 * i
a4 = 4 - 2 * i

[@MathswithChinwendu]

Thank you so much for sharing

[@georgesunaryo5080]

Keep it simple & stupid, just change the 16 into 2 square root 4.

[@MathswithChinwendu]

👍