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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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Range of $S = \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+..............+\frac{1}{\sqrt{n}}$

If $\displaystyle S = \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+..............+\frac{1}{\sqrt{n}}$ and $n\in \mathbb{N}$. Then Range of $S$ is $\underline{\bf{My \;\; Try}}$:: For Lower Bond:: $\sqrt{n}\geq \sqrt{r}\;\; \forall r\in…
juantheron
  • 53,015
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Reducing formula with factorials

I'm still a beginner working with factorials so, how should I reduce this formula i.e(cancel some member to make numbers smaller) ? $$\dfrac{(n^2)!}{4!(n^2 - 4)!\cdot Q}$$
aajjbb
  • 1,065
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Solve the equation $2^{3x+4} = 4 \sqrt 2$

Help?????? Before hand I had to write sqrt $2$ as a power of $2$ then express $4$ $\sqrt 2$ as a power of $2$. How to solve the above equation I am not too sure!?
Nicky
  • 41
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Reason for correct method of solving $x^6=x^4$ versus an erroneous method

when solving $x^6=x^4$ the correct points of intersection occur when solving in this manner: $x^4(x^2-1)=0, \Rightarrow x=0, x=\pm 1$ So, then why does attempting to solve the same problem via this way: $x^6=x^4$ then dividing $x^4$ from both sides…
veritas
  • 256
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Uses for the generalised f-mean, functions with larger/smaller f-means

What are some uses of the generalized f-mean outside of the geometric mean and the power means? Also, is there a known way to compare two functions and find out which will yield a larger f-mean (ex: we know that the function $f(x)=x^2$ will yield a…
yrudoy
  • 1,929
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fractional and integer system of equations

Solution for real ${a\;,b\;,c}$ in $a[a]+c\{c\}-b\{b\}=0.16$ $b[b]+a\{a\}-c\{c\} = 0.25$ $c[c]+b\{b\}-a\{a\} = 0.49$ Where $[x] =$ Integer part of $x$ and $\{x\} =$ fractional part of $x$ My try: I have add all three…
juantheron
  • 53,015
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5 answers

$a^2-b^2=37$, evaluate $ a^2+b^2$

Given $a^2-b^2=37$ and also a and b are integers, can we evaluate $a^2+b^2$ possible values? Are those many or just some? I found that $a^2+b^2$ can be only $685$. But how to prove it? I just guessed, but can we somehow evaluate it?
renathy
  • 339
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Can a term be its own coefficent in algebra?

I have a question in my math book; it asks me to find the coefficient of $b$ in the expression $3a+b+2c$. I thought, well, there is no coefficient of $b$, so I went on and then I wanted to go see if I was right at the back off the book and it says…
Zane willingham
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Help with simultaneous equation with additional term

I hoped someone can help me with 3 simultaneous equations with an additional condition. I can easily solve the following 3 equations using substitution in terms of $S_1$, $S_2$ and $S_3$" $$\begin{align*} \text{Eq 1)} &\qquad& (O_{1}-1)S_1 - S_2 -…
user12797
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3 answers

Roots of quartic equation - given product of two roots, find missing coefficient

The quartic equation $ax^4 + bx^3 + cx^2 + dx + e = 0$ has roots $\alpha, \beta, \gamma, \delta$. Given that $\alpha \beta = p$ find the value of $k$ So I have deduced that $\gamma \delta = \frac{e}{ap}$ using product of roots $=-\frac{e}{a}$ but…
PhysicsMathsLove
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Calculation of $\frac{n!}{1!+2!+3!+\cdots+(n-1)!}$

Calculation of $\displaystyle \left[\frac{n!}{1!+2!+3!+\cdots+(n-1)!}\right] = $ Where $n\geq 4$ and $n\in \mathbb{N}$ and $\left[x\right] =$ Greatest Integer of $x$ My Try :: For Upper Bond:: $n! = n.(n-1)! = \{(n-1)+1\}.(n-1)! =…
juantheron
  • 53,015
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Factoring $a^3-b^3$

I recently got interested in mathematics after having slacked through it in highschool. Therefore I picked up the book "Algebra" by I.M. Gelfand and A.Shen At problem 113, the reader is asked to factor $a^3-b^3.$ The given solution is: $$a^3-b^3 =…
bryanph
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Prove that roots are real

I am stuck with this equation, I need to prove the roots are real when $a, b, c \in R$ The equation is $$(a+b-c)x^2+ 2(a+b)x + (a+b+c) = 0$$ If someone could tell me the right way to go about this, so I can attempt it. Thank you EDIT: I have made an…
user
  • 938
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1 answer

What is the digit in the hundreds place of $5^{2017}$

What is the digit in the hundreds place of $5^{2017}$? Since $5^3 = 125$, powers with odd exponent of $5$, from the third onward, will end with the digits $125$, while those with even exponents will end with $625$. We can conclude that the digit…
Sebastiano
  • 7,649
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Is it possible to solve $2^{x} = x^{x} + x$ algebraically?

I came across the equation $2^{x} = x^{x} + x$ that was claimed to be only solvable via graphing or approximation. Is that the case, and if so why? I don't understand why the answer can't be described with operations.
Ammar Aldabbagh
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