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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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Need help with a power equation

If $x^3 + \frac{1}{x^3} = 52$, then what is $x^2 + \frac{1}{x^2}$? I'm not sure which formulae or methods should I used to solve this problem, so could somebody show me a way? what should I be looking for?
Karl
  • 875
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Prove that $ { a }^{ 2 }+2ab+{ b }^{ 2}\ge 0$ without using $(a+b) ^{ 2 }$

Prove that $${ a }^{ 2 }+2ab+{ b }^{ 2 }\ge 0,\quad\text{for all }a,b\in \mathbb R $$ without using $(a+b)^{2}$. My teacher challenged me to solve this question from any where. He said you can't solve it. I hope you can help me to solve it.
Science Addict
  • 327
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What is a "double zero" when I am trying to factor a quadratic equation?

A writing quadratic equations problem has a double zero of -1. I need to use this to find my two zeros and for a standard form equation.
Johnd
  • 205
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Solving $x^{x^{x^{x^...}}}=a$

Solving $$x^{x^{x^{x^...}}}=a$$ My attempt is $$x^{x^{x^{x^...}}}\log(x)=\log (a)$$ $$a\log(x)=\log(a)$$ $$x=a^{1/a}$$ that means I can select any value of $a$ to get the root,but when I selected some values, I found them not satisfy the original…
Samir
  • 111
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minimum $x^2 + y^2$ on $\frac{(x-12)^2}{16} + \frac{(y+5)^2}{25} = 1 $ ellipse

Given $\frac{(x-12)^2}{16} + \frac{(y+5)^2}{25} = 1$. Then minimum value of $x^2 + y^2 = ?$ P.S. My solution: Suppose that $x = 4\cos{\theta}+12$and $y = 5\sin{\theta}-5$ and expand $x^2 + y^2$ to find minimum value, but stuck in the end. Thank you…
ABCDEFG user157844
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How do I solve this problem?

Exercise: If $a+2b=125$ and $b+c=348$, find out $2a+7b+3c$. Here $a$, $b$, $c$ are natural numbers. The answer is: $2a+7b+3c = 1294$ I tried but just can't figure out how to get to this answer. I have a lot of exercises similar to this one but…
Klingon Duck
  • 53
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Why can I add the same number on both sides of an equation?

I know it is an elementary algebra question. But, is there a good reason for it being valid. Let's say we have $x+5=7$. We obviously know $x=2$, but if I can add any number on both sides and it still is valid. Ex: $x+5+3=7+3$. Simplifying to…
James Smith
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quadratic inequality

I do a procedure for solving algebraic inequalities of the second ($x^2+bx+c>0$) degree for my student. I know it is possible to solve the inequality by factorisation, Solving a quadratic inequality, see the first response by Casebash. I try another…
La Raison
  • 153
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The roots of $x^2-2x+3=0$ are $\alpha$ and $\beta$. Find the equation whose roots are: $\alpha+2$, $\beta+2$. Not sure of answer in book.

The roots of $x^2-2x+3=0$ are $\alpha$ and $\beta$. Find the equation whose roots are: $\alpha+2$, $\beta+2$. Not sure of answer in book. My working: $\alpha+\beta=2,…
shredalert
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Reversible and irreversible operations in elementary algebra

I am in high school algebra, solving typical equations such as rational, irrational, quadratic, etc., and I have come across the idea of extraneous solutions. My textbook does not touch upon the idea of extraneous solutions and how they relate to…
Wesley
  • 1,567
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Solving a simple rational equation $(\frac{6x}{6-x})^2+x^2=400$

Clearly we could multiply both sides of $$\left(\dfrac{6x}{6-x}\right)^2+x^2=400$$ by $(6-x)^2$ which leads to a degree 4 polynomial equation, which we can solve using the bi-quadratic formula. Moreover, we could approximate the solutions using…
userX
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Prove why the 'elimination method' of solving simultaneous equations works.

[This has been deleted due to me stressing out over something obvious that I didn't see; apologies if I seemed aggressive, I was merely stressed. Thanks.
BagelEnthusiast
  • 145
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How do you factor $\frac{2x^2-x-1}{x^2-9} \cdot \frac{x+3}{2x+1}=$?

\begin{align} & \frac{2x^2-x-1}{x^2-9} \cdot \frac{x+3}{2x+1}= \frac{2x^2-x-1}{(x-3)(x+3)} \cdot \frac{x+3}{2x+1} \\[10pt] = {} & \frac{2x^2-x-1}{(x-3)} \cdot \frac{1}{2x+1}= \frac{2x^2-x-1}{(x-3)} \cdot \frac{1}{2x+1}=…
user1068636
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Prove that: $ (a

Prove that: $$ (a
Gjekaks
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Calculate $S=3\sqrt{\sqrt[3]{5}-\sqrt[3]{4}}-\sqrt[3]{2}-\sqrt[3]{20}+\sqrt[3]{25}$

Calculate $$S=3\sqrt{\sqrt[3]{5}-\sqrt[3]{4}}-\sqrt[3]{2}-\sqrt[3]{20}+\sqrt[3]{25}$$ $\color{red}{\text{without using calculator}.}$ Please help me, I can't find any solution to sovle it.
mja
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