Princeton Math Interview Question | Can You Solve for ‘X’? | A Math Challenge of Wit and Wisdom

Get the Monthly Template + Instructions (How to use):
payhip.com/b/rw6kS
Get the Annual Template + Instructions (How to use):
payhip.com/b/qZjXg
.
.
.
Hey math lovers! Welcome to our comprehensive tutorial on solving intricate algebraic equations! In this video, we'll dive into the fascinating world of solving equations involving radicals, specifically tackling the challenging expression $x\sqrt {x\sqrt {x}}=3$.
With clear explanations and detailed examples, we'll break down each step of the solution process, making it easy for learners of all levels to follow along. From simplifying radicals to isolating variables, we'll equip you with the tools and strategies needed to confidently tackle even the most complex equations.
Whether you're a student brushing up on algebra skills or an educator looking for engaging teaching resources, this tutorial is perfect for you. Join us as we unravel the mystery behind radical equations and empower you to solve them with ease. Get ready to conquer your math challenges and elevate your problem-solving prowess!
TIMESTAMPS:
0:00 Introduction
0:08 Solution
4:08 Final answer
4:18 Practice question
4:38 Coupon code

[@user-xf3je3nt1p]

Substitution with y=sqrt(x) also works. But there are complex solutions too, x_k=3^(4/7)e^(i4kPi/7), k is Z [0, 6].

[@ingobojak5666]

Faster with logarithms: Take log on both sides. You get log x + 1/2 * log x + 1/4 * log x = log 3. Solves to log x = 4/7 * log(3) and thus x = 3^(4/7).

[@Tenraiden]

Nice music

[@pythondrink]

Imo, you unnecessarily complicated the problem
x^3 • √x = 9
Using the indicial law, namely that the nth root of a number is equal to that number to the power of 1/n, we can simply to:
x^3 • x^(1/2) = 9
x^{3+1/2) = 9
x^(7/2) = 9
Next, we raised both sides to the power of 2/7
x = 9^(2/7)
Ok what do I do now?

[@e.t.161]

You solved it as x = 9^(2/7) = 81^(1/7). Or just make ^4 on both sides of the equation. You get x^4 * x^2 * x = 3^4; x^7 = 81; x = 81^(1/7).

[@pythondrink]

@@e.t.161 I'm actually aware but I feltthere must be a way to simplify it further

[@Anoyzify]

9^(2/7), the 2 over there can be used to square the 9, becoming 81^(1/7).
Good approach.

[@maciejzettt]

Well, 3^(4/7) seems to be the simplest answer

[@JohnAmbruz]

Plodding ...