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
4
votes
3 answers

Novice question: what values of $x$ satisfy $\frac{x^2}{x} \le 0 $

Okay I'm embarrassed to even ask this clearly I am not going to win a Nobel prize in my life. Question What values of $x$ satisfy: $$\frac{x^2}{x} \le 0 $$ My attempt I'm very tempted to simplify the LHS and say the answer is $x \le 0$ But I have…
HJ_beginner
  • 1,715
4
votes
0 answers

Real root of $x(x+t)^2-4=0$ $\ge$ greatest real root of $4x^6-6x^4+4t^3x^3+t^6-3t^4=0$

I have a problem that I can not solve although I know that the statement is true. For all $t\ge0$ the real root of $x(x+t)^2-4=0$ is greater than or equal to the largest real root of $4x^6-6x^4+4t^3x^3+t^6-3t^4=0$. Does anyone have some idea to…
Piquito
  • 29,594
4
votes
2 answers

Algebraic Fractions

Hi I am struggling with solving this, I am 12 years old and am trying to work my way through extended maths IGCSE, but have been stumped by this for a few days: $\dfrac{13x + 2}{(2x + 1)(x - 1)} =\dfrac{A}{2x + 1} + \dfrac{B}{x - 1}$, what are the…
Hancho
  • 79
4
votes
2 answers

An algebraic equation; $ x^n -x =a $

Let $n\ge 2$ be an integer and $a$ be a real number such that $|a|\le (n-1)n^{-\frac n{n-1}}$. Can we find the real solutions of the algebraic equation $$ x^n -x =a. $$
Chung. J
  • 734
4
votes
1 answer

Why is $\frac{(x-1)+2}{(x-1)(x+1)} = \frac{1}{x-1}$?

According to the solution to a problem, the following equation holds true: $$\frac{(x-1)+2}{(x-1)(x+1)} = \frac{1}{x-1}$$ I can't see a way for this to work out.
Quispiam
  • 851
4
votes
3 answers

Implies sign in math

I get myself confused sometimes when to use => or = = x + y = x + 5 = x = -5 or => x + y => x + 5 => x = -5
user8218
4
votes
3 answers

How is $Ax + By = C$ the equation of a straight line?

I know the equation, $y = mx + b$ where $m$ is slope and $b$ is $y$-intercept, is a straight line. But I know also that $Ax + By = C$ is a straight line equation, but how does it represent a straight line?
user8218
4
votes
4 answers

Factorization of sum of two square

The difference is $a^2 - b^2 = (a - b).(a + b)$ But what about when I have $a^{25} + 1$ ? According to wolfram alpha, the alternate form is: $(a+1) (a^4 -a^3 + a^2 -a + 1)( a^{20} - a^{15} + a^{10} -a^5 +1)$ However, the square root of 25 is a…
danielsyn
  • 1,577
4
votes
1 answer

A simple inequality for floor function

If $x,y\in\mathbb R$, I have problems to show that $$\lfloor x\rfloor+\lfloor y\rfloor\le \lfloor x+y\rfloor\le \lfloor x\rfloor+\lfloor y\rfloor + 1 $$ Can someone help me?
Dubious
  • 13,350
  • 12
  • 53
  • 142
4
votes
0 answers

Factoring Polynomials with four terms and three variables

If $$\frac{x}{y} + \frac{y}{z} + \frac{z}{x} = 17,$$ then solve for $x$, $y$ and $z$, where $x$, $y$, and $z$ are positive integers. I got a common denominator of $xyz$, but then after that I was stuck: $$x^2z + xy^2 + yz^2 = 17xyz$$ I also…
azizj
  • 205
4
votes
1 answer

Prove the following polynomial equation has no answers

Assume there two polynomials for which the following equation$$P(Q(x))=Q(P(x))$$holds for $x\in\Bbb R$. Also the equation $P(x)=Q(x)$ has no real root. Prove that the following equation$$P(P(x))=Q(Q(x))$$has no real roots either. Sorry for having no…
Mostafa Ayaz
  • 31,924
4
votes
2 answers

$\max a^3+b^3+c^3+4abc$ sub $0\leq a,b,c \le 3/2$ and $a+b+c=3$

Let $S$ be the set of $(a,b,c) \in \mathbb{R}^3$ such that $0\leq a,b,c \leq \frac{3}{2}$ and $a+b+c=3$. Find $$ \max_{(a,b,c) \in S} a^3+b^3+c^3+4abc. $$
Fricul38
  • 711
4
votes
2 answers

Solve $x^4 -7x^3 + 4x^2 +39x -45=0$

Solve $x^4 -7x^3 + 4x^2 +39x -45=0$ I tried this question by using the products of roots $= -45 $. But factorization didn't go well. Trial and error method is not working. Please help me
user508848
4
votes
2 answers

Let $\log x=\log 2+\log y$ and $2^x+8^y=4$ then find the $x$

Let $\log x=\log 2+\log y$ and $2^x+8^y=4$ then find the $x$ My Try : $$\log x=\log 2+\log y \\ \log x=\log 2y \\x=2y $$ So we have : $$2^x+8^y=4\\2^{2y}+2^{3y}=4 \\t=2^y \\t^2+t^3=4$$ now what ?
Almot1960
  • 4,782
  • 16
  • 38
4
votes
4 answers

How much detail should be shown when writing out a problem?

When a somebody asks you to solve a problem and "show your work," how much detail should be shown? For a simple example, if I were to solve $5x+7=17$, should I…
Ian
  • 41
1 2 3
…
99 100