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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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Problem : What are our ages now?

Problem : My age was twice your age , when I was the same age as yours now. And when you are the same age as mine now , the sum of our ages is $63$ . What are our ages now? I see this problems in my teacher and solution is $(28,21)$ But I…
Ellen Ellen
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Find closest power of 2 to a specific number

This question is weird and it's not a homework question. I couldn't come up with anything substantial, so sorry if you think that I should have posted my tried methods (I have tried but most of them were fails). So, suppose I have a number $n$. Its…
Gaurav Mall
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Basic Algebra - Combining Like Terms

I am a self-taught software engineer who is finally getting back into math. So this is a basic question. The following expression: $-4(3w-u)-6(-4u-4w)$ confuses me. As I do not know why I should not solve it by SUBTRACTING $-4(3w-u)$ from the…
user434290
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How to solve $a\cos^2(\theta) + b \sin^2(\theta) = 0$ for $\theta$

How would I solve $$a\cos^2(\theta) + b \sin^2(\theta) = 0$$ for $\theta$. Here $a,b$ are constants and $a \neq b, a \neq 0, b \neq0$. I thought there might not be any solutions but with the constants $a,b,$ in front of them, I thought it is…
Kaish
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Square roots and cube roots equation

Solve over real $a$ $$\sqrt{3a-4}+\sqrt[3]{5-3a}=1.$$ If $p=3a-4$, $$\sqrt{p}+\sqrt[3]{1-p}=1.$$ If $q=5-3a$, $$\sqrt{1-q}+\sqrt[3]{q}=1.$$ Seems useful, but not sure how to proceed.
Baker013273213
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How to solve simultaneous two variable system

My maths knowledge is rusty and need some help in brushing it up. I tried to google around could not get what i am looking for How to solve the below equation $x + y = 6$ and $x^2 + y^2 = 20$ Help is greatly appreciated
linux developer
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Is Algebra Closed under all algebraic operations?

Note the following: If you take the set of integers $\mathbb Z$: and the operations of $+$ and $-$ Then all equations of the form ($x + a_1 + a_2 + a_3+\cdots+ a_N = b$) where $a$'s and $b$ are contained in $\mathbb Z$ has a solution in $\mathbb…
Sidharth Ghoshal
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Solutions to equation (or proof that there is no solution)

I am unable to find a solution or prove that there is none. I really need help: $a, b,$ and $c$ are positive integers such that $a^2-b^2+c^2=2.$ Is this possible? If possible find the solutions, if not prove that there is no solutions.
user686533
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solve the equation in $\Bbb C $

\begin{array}{l}{\text {Solve in } \mathbb{C}}: \\ {x^{2}+\left(\frac{x}{x+1}\right)^{2}=3} \\ {\text { my try: }} \\ {x^{2}(x+1)^{2}+x^{2}=3(x+1)^{2}} \\ {x^{2}\left(x^{2}+2 x+1\right)-3\left(x^{2}+2 x+1\right)+x^{2}=0} \\ ({x^{2}-3 )\left(x^{2}+2…
user373141
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If $x^y + y^x = 84$ and $x>3$, find the value of $x$ and $y$.

How do we go about this questions? I see that taking log on both sides is not an option since the LHS consists of a sum and not a product. I tried differentiating it but without any boundary conditions I fail to see any possible solutions. Can…
mathboggled
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Show that $x$, $y$, and $z$ are not distinct if $x^2(z-y) + y^2(x-z) + z^2(y-x) = 0$.

Suppose that $x^2(z-y) + y^2(x-z) + z^2(y-x) = 0$. How can I show that $x$, $y$, and $z$ are not all distinct, that is, either $x=y$, $y=z$, or $x=z$?
Peter Olson
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Simplify an equation where a fox chases a rabbit

I'm stuck on the following question and don't know how the book got its answer because it has multiple variables (its precalc so I don't know how to do calculus yet) and I don't know how to eliminate one completely. Any help is much…
maybedave
  • 509
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find array that this sum is the maximum

Hi Suppose that $n$ is a certain Natural number and $\{b_i\}_{i=0,..,n-1}$ is a certain array of positive real numbers, find array $\{a_i\}_{i=0,..,n-1}$ of positive real numbers such that $\sum_{i=0}^{n-1} a_i = 1$ and $\sum_{i=0}^{n-1} \sqrt {a_i…
saeedgnu
  • 183
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A car is moving at 40 km/h. A fly at 100 km/h, starts from wall towards the car(20 km away)flies to car and back. How many trips can it make?

A car is moving at a constant speed 40 km/h along a straight road which heads towards a wall.A fly flying at a constant speed of 100 km/h, starts from wall the towards the car at a instant when the car is 20 km away, flies until it reaches the car…
user541396
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How do I show that there exists a real number that equals its cube plus its square plus 1?

How do I show that there exists a real number that equals its cube plus its square plus 1? I was thinking $x = x^3+x^2+1$ then solve for $x$?
user7143
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