Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [algebra-precalculus]

For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

This tag is for questions typically taught in precalculus, as well as elementary algebra.

These topics include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomials, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

47234 questions
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8 answers

How to solve $x^3=-1$?

How to solve $x^3=-1$? I got following: $x^3=-1$ $x=(-1)^{\frac{1}{3}}$ $x=\frac{(-1)^{\frac{1}{2}}}{(-1)^{\frac{1}{6}}}=\frac{i}{(-1)^{\frac{1}{6}}}$...
user2723
25
votes
4 answers

Speed of two trains travelling side by side

I'm a high school student, and I have come across a problem that I cannot solve. I feel there must be something obvious that I'm not seeing. Problem: The distance between two train stations is $96$ km. One train covers this distance in $40$ minutes…
Vladislav Vordank
  • 365
25
votes
11 answers

Do values attached to integers have implicit parentheses?

Given $5x/30x^2$ I was wondering which is the correct equivalent form. According to BEDMAS this expression is equivalent to $5*\cfrac{x}{30}*x^2$ but, intuitively, I believe that it could also look like: $\cfrac{5x}{30x^2}$ I asked this question on…
Joe
23
votes
2 answers

Interesting Question on Ants

A horizontal stick is one metre long. Fifty ants are placed in random positions on the stick, pointing in random directions. The ants crawl head first along the stick, moving at one metre per minute. If an ant reaches the end of the stick, it falls…
Namch96
  • 918
22
votes
4 answers

Why dividing by zero still works

Today, I was at a class. There was a question: If $x = 2 +i$, find the value of $x^3 - 3x^2 + 2x - 1$. What my teacher did was this: $x = 2 + i \;\Rightarrow \; x - 2 = i \; \Rightarrow \; (x - 2)^2 = -1 \; \Rightarrow \; x^2 - 4x + 4 = -1 \;…
P.K.
  • 7,742
22
votes
6 answers

What are the possible values of these letters?

Out of all the questions I answered in a math reviewer, this one killed me (and 7 more). Let $J, K, L, M, N$ be five distinct positive integers such that $$ \frac{1}{J} + \frac{1}{K} + \frac{1}{L} + \frac{1}{M} + \frac{1}{N} + \frac{1}{JKLMN} =…
Heroic24
  • 317
22
votes
2 answers

Finding the roots of $(x^2+7x+6)^2 + 7(x^2+7x+6) + 6=x$

I have been trying to solve this one problem from the Duke Math Meet, which does not provide a solution: Find all solutions of $(x^2+7x+6)^2 + 7(x^2+7x+6) + 6=x$ At first I tried to factorize the polynomial, but always had the right-hand side $x$…
user462820
22
votes
5 answers

Purpose of Inverse Functions

Finding inverse functions and understanding their properties is fairly basic within mathematics. During my studies it was found fairly simple and easy to comprehend that it was a swapping of the outputs and inputs of a function. But now it has…
hubble
  • 619
22
votes
3 answers

Is there another way to solve this quadratic equation?

$$\frac { 4 }{ x^{ 2 }-2x+1 } +\frac { 7 }{ x^{ 2 }-2x+4 } =2$$ Steps I took: $$\frac { 4(x^{ 2 }-2x+4) }{ (x^{ 2 }-2x+4)(x^{ 2 }-2x+1) } +\frac { 7(x^{ 2 }-2x+1) }{ (x^{ 2 }-2x+4)(x^{ 2 }-2x+1) } =\frac { 2(x^{ 2 }-2x+4)(x^{ 2 }-2x+1) }{ (x^{ 2…
Cherry_Developer
  • 4,239
21
votes
7 answers

An oddity in some linear equations

Okay, so I've started Algebra I this year, and i've always had a love for math. And at one point in the course we were presented with an equation similar to this one: $5x + 3 = 8x + 3$ And so I solved it like such: $5x + 3 = 8x + 3$ $5x + 3 - 3 = 8x…
AlphaModder
  • 569
21
votes
7 answers

Solving $\sqrt{x+5} = x - 1$

I'm currently learning about radicals and simplifying them, and I came across this problem on the internet and tried to solve it: $$\sqrt{x+5} = x - 1$$ So I used this logic: $$ \begin{align} \sqrt{x+5} &= x - 1 \\ x + 5 &= (x-1)^2 \\ x + 5 &=…
Andreas Grech
  • 1,005
21
votes
8 answers

How to determine algebraically whether an equation has an infinite solutions or not?

I was learning for the first time about partial fraction decomposition. Whoever explains it, emphasises that the fraction should be proper in order to be able to decompose the fraction. I was curious about knowing what happens if I try to decompose…
StackExchange123
  • 341
20
votes
8 answers

Find $x$ such that $\sqrt{x+\sqrt{x+7}}\in \mathbb{N}$

Find $x$ such that $$\sqrt{x+\sqrt{x+7}}\in \mathbb{N}$$ I tried many ways: $$\sqrt{x+\sqrt{x+7}}=n$$ $$\sqrt{x+\sqrt{x+7}}^2=n^2$$ $$x+\sqrt{x+7}=n^2$$ then solve for $x$ but didn't do with success. I think this is the most difficult problem in my…
Geirg Von Kirk
  • 237
19
votes
6 answers

What are some other other examples similar to completing the square where a derived value is added and taken away again to create a useful form?

After 18 months of studying an advanced junior high school mathematics course, I'm doing a review of the previous 6 months, starting with solving difficult quadratics that are not easily factored, for example: $$x^2+6x+2=0$$ This could be processed…
duckegg
  • 669
19
votes
3 answers

Set of Elementary Real Numbers Without Elementary Combination

Find a set of $n$ real numbers such that none can be created by combining the others with elementary operations ($+, -, \times, /$). This question came up in my attempt to prove an $n$ dimensional version of the fundamental theorem of algebra;…
DreamConspiracy
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