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
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Where did I go wrong in completing the square?

$$2x^{ 2 }+8x+1=0$$ Move 1 to the other side of the equation: $$2x^{ 2 }+8x\quad =-1$$ Divide both sides by 2 to get 1 as the leading coefficient: $$x^{ 2 }+4x\quad =-\frac { 1 }{ 2 } $$ $$(\frac { 4 }{ 2 } )^{ 2 }$$ $$x^{ 2 }+4x+4\quad =-\frac { 1…
Cherry_Developer
  • 4,239
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Basic understanding of Log and $2 \log _3(x)+\log _9(x)=10$

So this is what I have done so fare $$2 \log _3(x)+\log _9(x)=10$$ I know that $$\log _9(x)=\log _3\left(\sqrt{x}\right)$$ I therefore have $$\log _3\left(x^{5/2}\right)=10$$ However here is where I realise that I have not properly understood the…
ALEXANDER
  • 2,099
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Stuck simplifying a fractional expression

$$ \frac { \frac { 1 }{ 1+x+h } -\frac { 1 }{ 1+x } }{ h } $$ $$ \frac { 1(1+x) }{ 1+x+h(1+x) } -\frac { 1(1+x+h) }{ 1+x(1+x+h) } $$ $$ \frac { -h }{ (1+x+h)(1+x) } \quad *\quad \frac { 1 }{ h } $$ This is what I have so far. I have no idea what…
Cherry_Developer
  • 4,239
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Find a real numbers $a,b$ such $a^n+b^n$ is rational

Question: prove or disprove :there exsit real numbers $a,b$ such follow two condition: (1):$a+b$ is irrational (2): for any postive integer $n\ge 2$, then $a^n+b^n$ is rational. I have know if $n=2k$ case is true,because I let…
math110
  • 93,304
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A math line interpretation

From the text of the question posed here: "How many whole numbers less than 2010 have exactly three factors?" this statement is made: If there is no fourth factor, then that third factor must be the square root of the number. Furthermore, that…
user52950
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What is the maximum y-value of the following function?

What is the maximum y-value of the following function? $$y=8t - \frac{t^2}{2} -24 $$ It can be done by using the parabolic equation , setting the equation is equal zero. But is there any other straight forward or shortest method to do this?
user52950
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Prove that $ \frac {12^{x-2}.4^{x}} {6^{x-2}} = 2^{3x-2} $

Can someone please help me with this question? $ \large \frac {12^{x-2}.4^{x}} {6^{x-2}} = 2^{3x-2} $ My steps so far: $ \large \frac {4^{x-2}.3^{x-2}.4^{x}}{3^{x-2}.2^{x-2}} = 2^{3x-2} $ $ \large \frac {4^{x-2}.4^{x}}{2^{x-2}} = 2^{3x-2} $ $ \large…
Dani
  • 53
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Algebra problem (deriving a variable in a formula)

How do I derive the $m$ in the formula: $$I=\left(1+\frac{r}{m}\right)^{mn} -1$$ all the values of the variables in the formula except $m$ is given and the question is find $m$. I just don't know how to derive the formula using the knowledge of…
user166417
  • 51
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How prove: $a=x$ and $b=x^x$ for $x^{a+b}=a^b b$?

Let $x, a, b$ natural numbers such that $x^{a+b}=a^b b$. How prove: $a=x$ and $b=x^x$?
piteer
  • 6,310
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Pythagorean triple means

Just out of curiosity, do there exist two positive integers whose arithmetic mean ($A $), geometric mean ($G $) and harmonic mean ($H $) constitute a Pythagorean triple? That is, $A $, $G $ and $H $ are positive integers, and $H^2 + G^2 = A^2$.
user27325
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1 answer

Simplify continued fraction with $\pi$

I'm not even sure where to start on this: Simplify: $$\pi+\dfrac{2}{\pi+\dfrac{2}{\pi +\dfrac{2}{\dots}}}$$ The second term is a rational expression with 2 in the numerator and the denominator is the entire expression again...over and over with no…
user163862
  • 2,043
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4 answers

Max. and Min. value of $|z|$ in $\left|z+\frac{2}{z}\right| = 2\,$

If $z$ is a complex no. such that $\displaystyle \left|z+\frac{2}{z}\right| = 2\,$ Then find max. and min. value of $\left|z\right|$. $\bf{My\; Try:}$ Given $\displaystyle \left|z+\frac{2}{z}\right| = 2\Rightarrow \left|z+\frac{2}{z}\right|^2 =…
juantheron
  • 53,015
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Solve $3^y=y^3,\space y\neq1,\space y\neq3$

I was messing around the other day and I noticed this: $2^3<3^2$ $2^4=4^2$ $2^5>5^2$ and I wondered if there is a pattern, i.e. $3^xz^3$ $x=y-1=z-2,\space y\neq1,\space y\neq3$ Then solve for $y$, and repeat with larger integers…
tomatopipps
  • 77
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If $a^3+b^3 = c^3+d^3$ and $a^2+b^2 = c^2 + d^2$, then $a + b = c + d$

I came across this problem today. I would be interested to see if anyone knows a proof for it: If $a^3+b^3 = c^3+d^3$ and $a^2+b^2 = c^2 + d^2$, then show that $a + b = c + d$.
icobes
  • 1,109
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Simple algebra formula for which I can't find the right answer

I have the formula $y + (z + 1) = \frac{1}{2} \cdot (z + 1) \cdot (z + 2)$, and I should work to $y = \frac{1}{2}\cdot z \cdot (z + 1)$. Somebody showed me how it's done: $y + (z + 1) = \frac{1}{2} \cdot (z + 1) \cdot (z + 2)$ $y + (z + 1) =…
Garth Marenghi
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