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
5
votes
2 answers

solving $12-x=\sqrt{12-\sqrt{x}}$

How can I slove: $12-x=\sqrt{12-\sqrt{x}}$? I tried to put $t=12-\sqrt{x}$ But it got me to polynomial of 4th degree which I don't think its the idea of solving this equation.
falcon
  • 75
5
votes
5 answers

intuition behind logarithm properties

A long time ago, I was taught that $\log(ab)=\log a + \log b$ and $\log(a/b)=\log a - \log b$ Then I was reminded of that from this answer on the site: Simple information theory question: where is this equation coming from? I have no problem…
bernie2436
  • 589
  • 2
  • 7
  • 17
5
votes
5 answers

no. of real roots of the equation $ 1+\frac{x}{1}+\frac{x^2}{2}+\frac{x^3}{3}+............+\frac{x^7}{7} = 0$

The no. of real roots of the equation $\displaystyle 1+\frac{x}{1}+\frac{x^2}{2}+\frac{x^3}{3}+............+\frac{x^7}{7} = 0 $ $\bf{My\; Try::}$ First we will find nature of graph of function $\displaystyle…
juantheron
  • 53,015
5
votes
2 answers

In the formula $Ax+By=C$, is it true that $A$ and $B$ can't both be zero? If so, why not?

I read in a math book that in the formula $Ax+By=C$, I read that $A$ and $B$ can't both be zero. I think C will also be zero because anything times zero equals zero and on a graph, the x- and y- intercepts will both be zero meaning the two points…
ReliableMathBoy
  • 968
5
votes
3 answers

How to solve $x^x=100$?

$x^x = 100$. I have no clue on how to solve this. If you guys have, please show me your solution as well.
Samborithy
  • 67
5
votes
4 answers

Removing the root squares from this expression?

I would like to understand how to remove the root squares from this expression: $$x = \frac 1{\sqrt{2} + \sqrt{3} + \sqrt{5}}$$ How to do it?
Zistoloen
  • 153
5
votes
3 answers

Solving an algebraic inequality

For any $a$, $b$, and $c$ prove $$3a^2+3b^2-2b+2a+1>0$$ I tried the following $$(a+1)^2+(b-1)^2+2(a^2+b^2)-1>0\\ (a+1)^2-1+(b-1)^2+2(a^2+b^2)>0\\ (a+1-1)(a+1+1)+(b-1)^2+2(a^2+b^2)>0\\ (a^2+2a)+(b-1)^2+2(a^2+b^2)>0\\ $$ $a^2$ and $(b-1)^2$ and …
max
  • 184
5
votes
2 answers

Why does the square root of a square involve the plus-minus sign?

If $\sqrt{x^2}$ can be simplified as follows: $\sqrt{x^2} = (x^2)^\frac{1}{2} = x^{\frac{2}{1}\times\frac{1}{2}} =x^\frac{2}{2} = x^1 = x$ Then why would $\sqrt{x^2} = \pm x$?
logsofrhythms
  • 177
5
votes
1 answer

Rationalizing a Denominator with Cube Roots

Rationalize $\dfrac{1}{\sqrt[3]{p^2}+\sqrt[3]{pq}+\sqrt[3]{q^2}}.$ How would I go about doing this without wading through lots of algebra? Is there a trick similar to how you can multiply by $\dfrac{\sqrt a-\sqrt b}{\sqrt a-\sqrt b}$ with square…
rk_347
  • 735
5
votes
2 answers

Best function getting 0 for odd parameter, 1 for even

I'm looking for two functions, assuming x is an integer: $$ f(x) = \begin{cases}0&\text{if x is odd}\\1&\text{if x is even}\end{cases} $$ and $$ g(x) = \begin{cases}1&\text{if x is odd}\\ 0&\text{if x is even}\end{cases} $$ For now I went up with…
PhilippeAuriach
  • 169
5
votes
1 answer

How can I calculate the VAT value from a given amount

I'm try to do a simple software but I need to understand the mathematical formula first... have a given amount, for example 499,00 how do I retrieve how much of a given VAT percentage (let's imagine 25%) I was thinking about the terms of: 499 =…
balexandre
  • 185
5
votes
1 answer

How many mappings $\phi:\Bbb{N}\cup\{0\}\to\Bbb{N}\cup\{0\}$ exist such that $\phi(ab)=\phi(a)+\phi(b)$?

How many mappings $\phi:\Bbb{N}\cup\{0\}\to\Bbb{N}\cup\{0\}$ exist such that $\phi(ab)=\phi(a)+\phi(b)$? My book says that the answer is finite. However, I am getting infinite as the answer. Let the prime numbers be mapped to any natural numbers…
algebraically_speaking
  • 259
5
votes
4 answers

question about double sums

Suppose we have an expression $$ \sum_{1 \leq k < j \leq n } f(k)f(j) $$ Can we express this as a double sum like $$ \sum_{k=1}^n \sum_{j=1}^n f(k)f(j) $$ ???
user195835
5
votes
3 answers

Find all integers $a$ for which $x^2-x+a$ divide $x^{13}+x+90$.

Find all integers $a$ for which $x^2-x+a$ divide $x^{13}+x+90$. The answer is $a=2$.
Satvik Mashkaria
  • 3,636
  • 3
  • 19
  • 37
5
votes
3 answers

Why do non-real solutions of a polynom occur pairwise complex-conjugated?

So if I have a polynom with real coefficients and the solution $x+iy$, why is $x-iy$ always a solution too? Let $z$ and $w$ be complex numbers, with $w^{\ast}$ = complex-conjugated of $w$, then $$(z-w)(z-w^{\ast}) = z^2 -2z\mathrm{Re}(w) +…
Christian
  • 1,781
1 2 3
…
99 100