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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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${\sqrt{2x+1}=1+\sqrt{x}}$ — I dont know if the solution is correct. Help?

${\sqrt{2x+1}=1+\sqrt{x}}$ ${2x+1=1+2\sqrt{x}+x}$ ${x=2\sqrt{x}}$ ${x*\frac{1}{x^{1/2}}=2}$ ${\sqrt{x}=2}$ ${x=4}$
Alyssa x
  • 135
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Find all possible values which following expression can take $\sqrt{x^2-7x+6}$

Given expression is: $\sqrt{x^2-7x+6}$. Now i first find values of x for which this is a valid question by putting guy inside square root equals to greater than 0. I get $x \in[-\infty,1]\cup[6,\infty] $. Now i completed the square and i got…
J. Deff
  • 1,588
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Find the remainder of a number when divided by $9$

Find the remainder when the number $$1234567891011121314151617\ldots200820092010$$ is divided by $9$. Show your work. I don't even know where to begin. Is there an underlying trick in finding the remainder of a number after being divided by $9$?…
Frank
  • 5,984
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Some numbers are sums of consecutive numbers. Which numbers can be written in more than one way?

As the title states: Some numbers are sums of consecutive numbers. Which numbers can be written in more than one way? For example numbers like $15$ can be written as $1+2+3+4+5$ or $7+8$ or $4+5+6$. What algebraic proof can be made to show which…
C.Keg
  • 53
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how to solve $x^2 = 3x + 4$

I am a programmer in the eighth grade taking algebra 1. I am only about a month into the school year, and I need to know how to solve something similar to this equation: $x^2 = 3x + 4$ However, the problem is that whenever I try to get the square…
tobahhh
  • 53
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1 answer

how does this simplify?

I am really stumped as to how it simplifies. I should know this, but it has been a very, very, long summer.
Kyle H
  • 557
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2 answers

Sum of powers of four

Let $0\leq a_1\leq a_2\leq\dots\leq a_n\leq b$ be integers such that $4^b\leq 4^{a_1}+\dots+4^{a_n}$. Can $4^b$ always be written as a sum of some subset of $4^{a_1},\dots,4^{a_n}$? I think it might be possible to perform some sort of greedy…
pi66
  • 7,164
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Showing that a function is bijective

Show that the function $f$ defined by $$f(x):=\frac{x}{\sqrt{x^2+1}}\;,$$ $x$ is an element of the reals, is a bijection of the reals onto $\{y:-1
Samuel Gregory
  • 291
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Integral value of $n$ that makes $n^2+n+1$ a perfect square.

Find all integers $n$ for which $n^2+n+1$ is a perfect square. By hit and trial we get $n=-1,0$ but could someone suggest any genuine approach as how to approach this problem?
MathGeek
  • 1,347
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Solving for $x$ of different powers

I want to solve the following equation for $x$ $$\left(x + \frac{6}{x} \right)^2 + \left( x + \frac{6}{x} \right) = 30$$ I done my working till - $$x^4 + x^3 - 18x^2 + 6x + 36 = 0$$ From here how do I solve for $x$ when I have any different powers…
user307640
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What is the value of $\frac{a^2}{b+c} + \frac{b^2}{a+c} + \frac{c^2}{a+b}$ if $\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} = 1$?

If $$\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} = 1$$ then find the values of $$\frac{a^2}{b+c} + \frac{b^2}{a+c} + \frac{c^2}{a+b}.$$ How can I solve it? Please help me. Thank you in advance.
user251057
5
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2 answers

Solve / Simplify for x

$$\frac{1}{\sqrt{a^{2}-x^{2}}}+\frac{1}{\sqrt{b^{2}-x^{2}}}-\frac{1}{c}=0$$ Hello I'm wondering whether anyone can help me rearrange this to solve for $x$, where $a$, $b$, $c$ are constants. I initially thought about a trig substitution $x=b\cdot…
Guy
  • 51
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Dimensional Analysis basic question.

I had a pretty basic question about dimensional analysis. According to this site : "Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be…
king9x
  • 91
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4 answers

Basic clarification: Solving equation by squaring, but end up getting non-existent answers

This is going to be extremely elementary given the caliber of questions being posted. I was going over something basic and think I'm overlooking an extremely fundamental rule. $$2x-1 = \sqrt{6x+1}$$ By inspection, the solution is x=5/2. However, to…
sahimat
  • 532
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1 answer

Value of $k$ for equation to have no solution

What are different integer values of $k$ between $1-9$ for which the equation $$|x-1|+|x-2|+|x+1|+|x+2|=4k$$,has no solutions. Now there are 24 different ways of having signs ie the equation after removing mod.solving these $24$ equations and then…
Archis Welankar
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