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
3
votes
5 answers

Solve the logarithmic equation: $\log_2(x^2 − 5x − 28) = 3$

I distributed the the log $$\log_2 x^2 - \log_2 2x - \log_2 27 = 3$$ but I am stuck at that point. Any hints?
Cetshwayo
  • 3,092
3
votes
1 answer

$x^5+x-1=0\;,\;x\in\mathbb{R}$

Given the following equation $$x^5+x-1=0\;,\;x\in\mathbb{R}$$ How to prove that (unevaluated) $$x=\dfrac13\left(-1+\sqrt[3]{\dfrac{25}2-\dfrac{3\sqrt{69}}2}+\sqrt[3]{\dfrac12\left(25+3\sqrt{69}\right)}\right).$$ $x^5+x-1=0\;,\;x\in\mathbb{R}$ Any…
felipeuni
  • 5,080
3
votes
0 answers

Tricks to simplify the expression

I tried to prove Routh's theorem from geometry and while solving it I had to simpily $$1-\frac{s}{st+s+1}-\frac{t}{rt+t+1}-\frac{r}{rs+r+1}$$ to $$\frac{(rst-1)^2}{(st+s+1)(rt+t+1)(rs+r+1)}$$ I managed to do it by multiplying everything out and…
geometryfan
  • 31
3
votes
3 answers

Find x in $4^{\sin^2x}+4^{\cos^2x}=8$

$$4^{\sin^2x}+4^{\cos^2x}=8$$ I solved like this: \begin{align*}4^{\sin^2x}+4^{\cos^2x}=8&\Rightarrow4^{\sin^2x}+4^{1-\sin^2x}=8\\ &\Rightarrow4^{\sin^2x}+\frac{4}{4^{\sin^2x}}=8…
Daniel
  • 463
3
votes
1 answer

Recipe for solving equations

I am making a script that's solving algebra. I am 16 years old so my script should be able to solve all middle school equations. (Because this is the level I have when it comes to maths. Got the grade: A) Do anyone have a complete recipe that would…
Friend of Kim
  • 292
3
votes
2 answers

Solving $x-\sqrt{(x^2-36)} = {(x-6)^2\over 2x+12}$.

I have problem with this equation: $$x-\sqrt{(x^2-36)} = {(x-6)^2\over 2x+12}$$ Any ideas on beatiful solving?
user157837
  • 33
  • 2
3
votes
1 answer

Proving all numbers in Pascals triangles are natural numbers by induction

I am working on this proof from my book, and I believe to have solved it. However, proof by inductions still feel funny to me and this question uses more than one variable, so I'm not sure if I have done it correctly. I could not find the answer…
Jason
  • 3,563
3
votes
1 answer

Why applying this algebraic logarithm identity changes the function output?

I have fear this is an extremely ridiculous and basic question. But let's say we have $f(x) = \ln(x^2)$ by applying one of the most basic identities for logarithms, it should be possible to say that $f(x) = \ln(x^2) = 2 \ln(x)$ However, it seems…
user157419
  • 31
  • 1
3
votes
1 answer

How to sum results of repeated subtraction

Trying to teach myself maths and I realise this is a very basic question (and probably a basic concept), but I don't know how to express what I'm looking for (my Google skills are letting me down...) If I wanted to repeatedly subtract n from a, I…
user2781522
  • 33
  • 2
3
votes
5 answers

Factor the Expression completely$ (a+b)^2 - (a-b)^2$

I don't understand this question. The answer in the book is $4ab$, but how is that term a factor? I was thinking along the line that this was a difference of squares example. $a^2-b^2 = (a+b)(a-b)$ My answer is $[(a+b)-(a-b)][(a+b)+(a-b)]$ What do I…
Cetshwayo
  • 3,092
3
votes
1 answer

Finding an inverse function

I'd like to make sure I'm doing things right, my answer looks a little funny. I have the following function: $$g(x) = 3 + x + e^x$$ I am trying to find $g^{-1}(x)$, so I replace $g(x)$ with $y$ and switch it with $x$ to get: $$x = 3+y + e^y$$ I get…
Irresponsible Newb
  • 1,323
3
votes
2 answers

Systems of equations with three variables

Consider: $a + b = 5$ $2a + b + c = 4$ $a - b - c = 5$ I like to use substituiton for solving systems of equations, so I firstly look at equation 1 and solve for $a$ $a + b = 5$ $a = 5 - b$ I substitute this into equation 2 $2(5-b) + b + c = 4$ $10…
xvzz
  • 29
  • 1
3
votes
1 answer

positive values of $a$ for which the equation $\lfloor x+a \rfloor = \sin \left(\frac{\pi x}{2}\right)$ will have no solution

The positive values of $a$ for which the equation $\displaystyle \lfloor x+a \rfloor = \sin \left(\frac{\pi x}{2}\right)$ will have no solution is, where $\lfloor x \rfloor = $ floor function of $x$ …
juantheron
  • 53,015
3
votes
2 answers

Expand $(x-7)^2 + x^2 = (x+2)^2$ algebraically

$(x-7)^2 + x^2 = (x+2)^2$ $(x-7)(x-7) + x^2 = (x+2)(x+2)$ $x^2 -7x -7x + 49 + x^2 = x^2 + 4x + 4$ $x^2 + 18x - 45 = x^2 + x^2$ From that point on, everything I do is incorrect. I don't know what to do with the three $x^2$.
Alatma
  • 93
3
votes
1 answer

Simplifying equation of a parabola

The text defines the equation of a parabola as: $\sqrt{x^2+(y-p)^2}=y+p$ where $y$ is the y coordinate of a point on the parabola and $p$ is the y coordinate of the focus. It goes on to say: By squaring and simplifying we get $x^2=4py$. I'm trying…
Nick
  • 647
1 2 3
…
99 100