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
4
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3 answers

minimum value of $f(t) = 10t^6-24t^5+15t^4+40t^2+108$ without derivative

minimum value of $f(t) = 10t^6-24t^5+15t^4+40t^2+108$ without derivative for $t\leq 0$ value of function $f(t)\geq 108$ i wan,t be able to proceed after that ,could some help me with this
DXT
  • 11,241
4
votes
1 answer

GRE algebra question, evaluate the expression

Given x,y<0, What is the value of $$\frac{\sqrt{x^2}}{x} - \sqrt{\frac{-y}{\left\lvert y \right\rvert}}$$ Since $x$ and $y$ are negative that means the first term should reduce to $$\frac{\left\lvert x \right\rvert}{x}$$ and the second term…
Frank Shmrank
  • 440
4
votes
1 answer

Is something wrong with this precalculus question?

If $x^{2}-4x+6=0$, then what can be the value of $1-\frac{4}{3x}+\frac{2}{x^{2}}$? My answer is $1-\frac{4}{3x}+\frac{2}{x^{2}}=\frac{3x^{2}-4x+6}{3x^{2}}=\frac{3x^{2}-x^{2}}{3x^{2}}=\frac{2}{3}$ for $x\neq 0$. But according to the book answer is 2.…
user315531
  • 663
4
votes
4 answers

Which quantity is bigger (practice GRE question)

Given, x is a real number Quantity A: $$(x-2)(x-4)(x+5)$$ Quantity B: $$(x-5)(x^2+5x+5)+68$$ The first thing I did was to expand Quantity B and after combining like terms I get $$x^3-20x+43$$ Since $43$ is prime I can't (I don't think) factor that…
Frank Shmrank
  • 440
4
votes
6 answers

How to prove there are no solutions to the equation $a^2-4ab+b^2=0$ if $a$ and $b$ are real numbers and $b \neq 0$?

I am trying to prove $a^2-4ab+b^2=0$ has no solutions for all real numbers $a$ and $b$ and $b \neq 0$ My attempt: We know that $a^2 \geq 0$ and $b^2 > 0$ since $b \neq 0$. So then $a^2 + b^2 >0$. Now I'm stuck as I'm not sure how to show that $a^2 +…
Aspiring Mathlete
  • 2,312
4
votes
2 answers

System of five equations

I'd really appreciate help with this problem, because I'm stuck with it. $$ \left\{ \begin{array}{c} ab+ac+ad+ae=-1 \\ ba+bc+bd+be=-1 \\ ca+cb+cd+ce=-1 \\ da+db+dc+de=-1 \\ ea+eb+ec+ed=-1 \end{array} \right. $$ I've tried substituting…
suomynona
  • 297
4
votes
3 answers

maximum value of $xy+yz+zx.$ given $x+2y+z=4$

if $x+2y+z=4$ and $x,y,z$ are real number. then find maximum value of $xy+yz+zx$ putting $x+z=4-2z$ in $y(x+z)+zx = y(4-2z)+zx = 4y-2yz+zx$ i wan,t be able to go further,could some help me with this
DXT
  • 11,241
4
votes
7 answers

Solve for $n$ in $18^{n+1} = 2^{n+1} \cdot 27$

Solve for $n$: $$18^{n+1} = 2^{n+1} \cdot 27$$ I tried: $$18^{n+1} = 2^{n+1} \cdot 27 \Leftrightarrow 18^n \cdot 18 = 2^n \cdot 54 \Leftrightarrow \frac{18^n}{54} = \frac{2^n}{18} \Leftrightarrow \frac{18 \cdot 18^n - 54 \cdot 2^n}{972} = 0…
Mark Read
  • 2,183
4
votes
0 answers

Gain or Loss in simple way?

A person sells an article at a profit of 10% If he had bought it at 10% less and sold it for 3 dollars more ,he would have gained 25%.Find the Cost price. My solution is 120 I derived to the solution by fraction method let $x$ be the cost price…
Bharad Waj
  • 107
4
votes
2 answers

Squaring gets puzzled.

$ x = \sqrt{1} $ then x = ? and $ x^2 = 1 $ then x = ? please help I am puzzled. I know that in first case we will get x = 1 and in second case we will get x = $ \pm 1 $ But, I need the proof for the first case.
Kushashwa Ravi Shrimali
  • 1,412
4
votes
2 answers

real values of $a$ for which the range of function $ f(x) = \frac{x-1}{1-x^2-a}$ does not contain value from $\left[-1,1\right]$

All real values of $a$ for which the range of function $\displaystyle f(x) = \frac{x-1}{1-x^2-a}$ does not contain any value from $\left[-1,1\right]$ $\bf{My\; Try::}$ Let $\displaystyle y = \frac{x-1}{1-x^2-a}\Rightarrow y-x^2y-ay=x-1$ So…
juantheron
  • 53,015
4
votes
1 answer

Deriving numbers from sums

Let $x_1,\dots,x_n$ be not necessarily distinct real numbers. Form a multiset $A$ by taking the $2^n-1$ sums of nonempty subsets of the numbers. For example, if we have $(x_1,x_2,x_3)=(1,2,-3)$, then by taking the seven sums,…
pi66
  • 7,164
4
votes
4 answers

I think there is an error in this solution

I have been trying to reconcile this solution with my work for hours now. Could someone please help me confirm whether the solution provided below is incorrect? I get a solution of X > -3/2, the provided solution is X < 3/2
Heidi Good
  • 65
4
votes
3 answers

Find $m$ and $n$ so that the given function has the range $[-3, 5]$

Find $m$ and $n$ real numbers so that $f(x) = \frac{3x^2 + mx + n}{x^2 + 1}$ takes all and only the values from the interval $[-3, 5]$. I started by solving the following double inequality: $$-3 \leq \frac{3x^2 + mx + n}{x^2 + 1} \leq 5$$ From the…
George R.
  • 2,833
4
votes
3 answers

How come there is only one solution to $\sqrt{110-n} = n$

Given: $\sqrt{110-n} = n$ It follows that: $110 - n = n^2$ $n^2 + n - 110 = 0$ $(n + 11)(n - 10)=0$ If $n = 10$, $\sqrt{110 - 10} = \sqrt{100} = 10$, it checks out. If $n = -11$, $\sqrt{110 - (-11)} = \sqrt{121} = 11$, it doesn't However! I thought…
Henry
  • 517
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