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.

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How to distinguish $y^2=(x+a)(x-b)^2$ from $y^2=(x+a)(x-b)^4$ if a graph is given?

From the following question, I understood that the answer must be one of options c and f. The other options are wrong (I will not explain why). Question How can I decide the correct answer from the left options (c and f)? Edit I plotted both with…
Display Name
  • 2,715
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Solve for non-linear system of equations without computer

Find $a,b,c \in \mathbb R$ such that: $$\left\{ \begin{align} a+b+c &=4 \\ \left( a+b \right) \left( b+c \right) \left( c+a \right) &=18 \\ \frac 1 a+\frac 1b+\frac 1c &=\frac 52 \end{align} \right.$$ How do I solve for $a,b$ and $c$ manually…
Xeing
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Spivak, Calculus, Chapter 1, Problem 19b: how to gain intuitive understanding of this proof of the Schwarz Inequality?

In the Prologue section of Spivak's Calculus, Ch.1 problem 19b, we are asked to prove Schwarz inequality starting from the inequality $$2xy\leq x^2+y^2\tag{1}$$…
xoux
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Solving $\frac{(1+x)(1+2x)(1+3x)}{(4+x)(4+2x)(4+3x)}=4 $. Simply bringing it to a common denominator does not lead me to success

How can I solve this equation? $$\frac{(1+x)(1+2x)(1+3x)}{(4+x)(4+2x)(4+3x)}=4 $$ Simply bringing it to a common denominator does not lead me to success What I tried
sleepydogbark
  • 43
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Given that $ x + \frac 1 x = r $ what is the value of: $ x^3 + \frac 1 {x^2}$ in terms of $r$?

Given that $$ x + \cfrac 1 x = r $$ what is the value of: $$ x^3 + \cfrac 1 {x^2}$$ in terms of $r$? NOTE: it is $\cfrac 1 {x^2}$ and not $ \cfrac 1 {x^3} $ Where I reached so far: $$ \Big(x^3 + \cfrac 1 {x^2}\Big) + \cfrac 1 x \cdot\Big(x^3 +…
Parth Thakkar
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Algebra equation for percentage increase needed to get the current value as a 20% discount

I have some products that I want to increase in value such that a 20% discount gives their current value. It's been ~25 years since college algebra and so I'm a bit rusty on setting up the equation. I've been trying to figure out how to solve for X…
Chuck Savage
  • 143
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Converting Ranges

I am writing a program for the arduino that takes a number as input and displays colors based on that input. At any given time, I know the value of the variables min and max where min is the minimum value of the input range and max is the maximum…
Max Isom
  • 43
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What is the solution if $a=1$

We have the equation $$x_n = a^nx_0+b\,\left(\dfrac{1-a^n}{1-a}\right).$$ I had to find the solution if $a=1$ and $a=-1$ For $a=1$ we must divide by $0$ which is of course impossible, but I wonder; does that render $a=1$ 'solutionless' or does that…
iEvenLift
  • 117
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Solving $4=2^{x^{x^{x^{x^{...}}}}} $ for $ x$

Is it possible to solve the following equal for $x$? $$4=2^{x^{x^{x^{...}}}}$$ I'm bit confused, how do you even simplify this equation, factoring?
user82528
  • 75
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How to expand and simplify $(p^y * (pq)^o) / (p^{(2y+o)} * q^{(o-2)})$?

I'm a beginner to maths and have trouble simplyfying the following function: $$\frac{p^y \cdot (pq)^o}{p^{2y+o} \cdot q^{o-2}}$$ The final answer is $$p^{-y} \cdot q^2$$ But I'm not sure how to get there. Any help is appreciated.
Tom
  • 185
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Decimal pattern in division of two digit numbers by 9

Can some one explain how this is possible ? 1) 13 / 9 = 1.(1 + 3) = 1.444 ... 2) 23 / 9 = 2.(2 + 3) = 2.555 ... 3) 35 / 9 = 3.(3 + 5) = 3.888 ... 4) 47 / 9 = 4.(4 + 7) = 4.(11) → 4.(11 - 9) = 5.222 ... 5) 63 / 9 = 6.(6 + 3)…
Sudheej
  • 155
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Solve $ax - a^2 = bx - b^2$ for $x$

Method 1 Solve for x $$ax - a^2 = bx - b^2$$ Collect all terms with x on one side of the equation $$ax - bx = a^2 -b^2$$ Factor both sides of the equation $$(a -b)x = (a+b)(a - b)$$ Divide both sides of the equation by the coefficient of $x$ …
user 85795
  • 1,659
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Is $\frac{1-\alpha}{1+\alpha}=y \Rightarrow \alpha=\frac{1-y}{y+1}$ correct even if $y=-1$?

I was trying to solving this question: If roots of the equation $a x^{2}+b x+c=0$ are $\alpha$ and $\beta$, find the equation whose roots are $\frac{1-\alpha}{1+\alpha}, \frac{1-\beta}{1+\beta}$ I was not able to solve it so I looked to the…
Osmium
  • 379
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Find the values of the constants in the following identity $2x^3+3x^2-14x-5=(ax+b)(x+3)(x+1)+C$

I'm working through identities but I can't figure out how to get further than multiplying out the above to get : $$2x^3+3x^2-14x-5=2ax^3+3ax^2+3ax+bx^2+3bx+bx+3b+C$$ can someone give me a hint on what to do next?
peter_gent
  • 99
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What is the defining characteristic of a quadratic function?

I'm helping a high school student prepare for an exam, and I'm unsure how to answer this... Why is $x^3+2x^2$ not quadratic? I thought anything that had a power of 2 was quadratic.
Mirrana
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