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
8
votes
6 answers

Repeated Decimal Expansion Corresponding to a Fraction Problem

How do I solve the following question. The repeated decimal expansion $1.23\overline 6$ corresponds to which fraction? a. $\frac{370}{300}$ b. $\frac{3710}{3001}$ c. $\frac{371}{301}$ d. $\frac{37100}{30001}$ e. $\frac{371}{300}$ Here is how I…
jesse
  • 81
8
votes
4 answers

How do you solve $[x]+[2x]+[3x]=4x$ on $\Bbb R$?

Find the arithmetic average of all solutions $x\in\Bbb R$ of the equation $$[x]+[2x]+[3x]=4x,$$ where $[x]$ denotes the integer part of $x$ (e.g. $[2.5]=2$, $[-2.5]=-3$). I tried solving this problem by looking at $\{x\}$ and writing for…
Falcon Rhymes
  • 83
8
votes
4 answers

How to simplify $42\sqrt{45} \over 7\sqrt{35}$?

The problem is $$42\sqrt{45} \over 7\sqrt{35}$$ HELP! My daughter's math sheet shows how to reduce the squareroots, but the examples all use the same square-root; the problems show two different numbers square-rooted. Can you please help work this…
Maureen Murphy
  • 83
8
votes
3 answers

How to solve equation $ \frac{1}{2} (\sqrt{x^2-16} + \sqrt{x^2-9}) = 1$?

$$ \dfrac{1}{2} (\sqrt{x^2-16} + \sqrt{x^2-9}) = 1$$ How can I solve this equation in the easiest way?
Birdistheword
  • 115
8
votes
5 answers

How to factor $a^{3} + b^{3} + c^{3} - 3abc$ into a product of polynomials

The question is in the title. This question is from "Algebra" by Gelfand. My initial thought is that if $a$, $b$ and $c$ are $1$ or $-1$, then the polynomial evaluates to $0.$ So, maybe two of the factors will be $(a + b + c - 3)$ and $(a + b + c +…
ski
  • 107
8
votes
1 answer

$f(x)=x^3+ax^2+bx+c$ has roots $a,b$ and $c$

How many ordered triples of rational numbers $(a,b,c)$ are there such that the cubic polynomial $f(x)=x^3+ax^2+bx+c$ has roots $a,b$ and $c$? The polynomial is allowed to have repeated roots.
Raj
  • 83
  • 1
  • 4
8
votes
4 answers

Solving for unknown

When solving for unknowns why does the symbols sometimes change from $a + $ to $a -$ or vice versa or stays the same? For example (using solutions from text): $2x+6 = x+16\quad$ and the solution is $2x-x = 16-6\quad \Rightarrow \quad…
Dan
  • 81
8
votes
2 answers

Solve $x^2+2ax+\frac{1}{16}=-a+\sqrt{a^2+x-\frac{1}{16}} $

Find the real roots of the equation $$x^2+2ax+\frac{1}{16}=-a+\sqrt{a^2+x-\frac{1}{16}} $$ $$(0
Mathxx
  • 7,570
8
votes
2 answers

Prove: If $x+y+z=xyz$ then $\frac {x}{1-x^2} +\frac {y}{1-y^2} + \frac {z}{1-z^2}=\frac {4xyz}{(1-x^2)(1-y^2)(1-z^2)}$

If $x+y+z=xyz$, prove that: $$\frac {x}{1-x^2} +\frac {y}{1-y^2} + \frac {z}{1-z^2}=\frac {4xyz}{(1-x^2)(1-y^2)(1-z^2)}$$. My Attempt: $$L.H.S=\frac {x}{1-x^2}+\frac {y}{1-y^2}+\frac {z}{1-z^2}$$ $$=\frac…
pi-π
  • 7,416
8
votes
6 answers

The sum of digits in a 2-digit number

The sum of digits in a two digit number formed by the two digits from $1$ to $9$ is $8$. If $9$ is added to the number then both the digits become equal. Find the number. My attempt: Let the two digit number be $10x+y$ where, $x$ is a digit at…
pi-π
  • 7,416
8
votes
3 answers

An equation with two variables is unsolvable for either one, but how can I know if it's unsolvable as an expression for both?

Weird title perhaps, so let me illustrate with the question that got me thinking about this problem: You are buying a laptop and have two to choose from. What is the difference between the original prices of the two laptops? What you know: After…
Yeats
  • 387
8
votes
4 answers

Solve $(\sqrt{5+2\sqrt{6}})^{x}+(\sqrt{5-2\sqrt{6}})^{x}=10$.

Solve $(\sqrt{5+2\sqrt{6}})^{x}+(\sqrt{5-2\sqrt{6}})^{x}=10$ I square the both sides and get $(5+2\sqrt{6})^{x}+(5-2\sqrt{6})^{x}=98$. But I don't know how to carry on. Please help. Thank you.
JSCB
  • 13,456
  • 15
  • 59
  • 123
8
votes
6 answers

Why I can't divide by y in this equation: 4y = y?

I have this equation $$ 4y = y $$ If I divide by y in both sides I would get this: $$ 4 = 1$$ And this does not have sense. I know that the solution is 0 but why I get this answer when dividing by y. What's the logic behind?
Javier Cárdenas
  • 199
8
votes
2 answers

Algebra solve for $x$ in the equation $x^3 = x$

I tried to solve for x in the equation $x^3=x$. I did $$x^3=x$$ $$x^2=1$$ $$x=\pm1$$ but it's wrong, can anyone help.
thunderbolt
  • 767
8
votes
1 answer

The intersection of two conics - matrix solution

I recently had to compute the intersection of two conics, and found it to be a long and complicated procedure. Looking at Wikipedia, the advice to find the points of intersection of two conics in general, which is echoed in the answer to this…
mboratko
  • 4,553
1 2 3
…
99 100