r/mathbiceps

In about a month, I will be sitting for my college entrance exam, and I have been practising with previous years' questions from that college. While doing so, I came across this equation:

4x^6+3x^5+2x^4=384

The question simply asks for the value of x, and there is only one answer needed. The problem is that my calculator is a Casio FX-991CW, which is the most powerful calculator permitted in the exam. It is non-programmable, but when I use its equation-solving functions for this problem, it takes roughly 55 seconds to obtain the answer, which is far too long for an entrance exam where time is critical.

The answer is x=2.

I asked some seniors how they solved it. They treated the left-hand side as a polynomial,

P(x)=4x^6+3x^5+2x^4,

and simply evaluated P(1), P(2), etc. Since P(2)=384, they immediately got x=2.

The difficulty I have with this method is that it relies heavily on guessing small integer values. What if a similar question had an answer such as

x= -1/3, x= -2, x= 1/4

or some other non-obvious value? Since this is not an MCQ, I cannot simply test the answer choices. So my question is:

What algebraic tricks or patterns would you use to solve this sort of equation quickly, with very little writing, in a college entrance exam?

I would be grateful for any efficient techniques or general patterns worth learning for this kind of problem.

Real numbers a,b,c satisfy ab-c=a, bc-a=b, ac-b=c. What is the sum of all possible values of (a+1)(b+1)(c+1) ?

Godzilla question

480 IQ question

This question is not solve for AI

Isko solve karne mein ek hi niyam ka upyog Kiya jata hai

3²=36

4²=55

5²=102

6²=402

7²=?

18²=?

My name is a Prajapati Kalpesh Kumar Ramesh Kumar

I am a 13 year old

Your challenge kya tum mujhse solve kar sakte ho ya nahi

Let P(x) = x ^ 2 + bx + c be a quadratic polynomial with real coefficients. If the equation P(P(x)) = 0 has four distinct real roots, and the sum of two of these roots is -1 , while the product of the remaining two roots is also fixed, what absolute conditional bound must the discriminant of P(x) satisfy?

(A) b ^ 2 - 4c > 2

(B) b ^ 2 - 4c > 4

(C) b ^ 2 - 4c > 0

(D) b ^ 2 - 4c > 8

The problem was already shared in this sub-reddit, this is the solution video for the same