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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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Solve $\sqrt{x-4} + 10 = \sqrt{x+4}$

Solve: $$\sqrt{x-4} + 10 = \sqrt{x+4}$$ Little help here? >.<
Inception
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functions with floors

If $$z = \frac{ \left\{ \sqrt{3} \right\}^2 - 2 \left\{ \sqrt{2} \right\}^2 }{ \left\{ \sqrt{3} \right\} - 2 \left\{ \sqrt{2} \right\} }$$ find $\lfloor z \rfloor$. I don't rely know how to do this, but I was thinking about multiplying the…
clache547
  • 129
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Algebra Problem: $a + 1/b = b + 1/c = c + 1/a = t $

a, b, c are distinct reals such that $$a + 1/b = b + 1/c = c + 1/a = t $$for some real t. Show that t = -abc I tried using continued fractions to isolate a,b and c but equations of degree more than 2 are formed.
420
  • 45
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Quadratic Inequality in terms of variable $x$

Find the values of $a$ for which the inequality $x^2+ax+a^2+6a<0\;\forall x \in (1,2)$ $\bf{My\; Try::}$ We can Write Equation as $$x^2+ax+\frac{a^2}{4}+\frac{3a^2}{4}+6a<0$$ So $$\left(x+\frac{a}{2}\right)^2+\frac{3a^2+24a}{4}<0$$ Now how can i…
juantheron
  • 53,015
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Algebraic Expressions with Fractions

can someone review this and see if i've done it correctly please. $$\frac{\frac {3x} {y}}{\frac {2x}{7}} $$ $$= \frac{3x}{y} . \frac{7}{2x}$$ $$= \frac{21x}{2xy} $$ $$= \frac {21}{2y} $$ Thank you for your time.
Aeonify
  • 71
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If $5\sqrt [ x ]{ 125 } =\sqrt [ x ]{ { 5 }^{ -1 } } $, then $x$ equals $-4$

For the equation $$5\sqrt [ x ]{ 125 } =\sqrt [ x ]{ { 5 }^{ -1 } } $$ $x$ is equal to $-4$, but I'm not sure why. I've taken the right side of the equation ${ \left( \frac { 1 }{ 5 } \right) }^{ \frac { 1 }{ x } }$ and converted it to…
maudulus
  • 213
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How many times do runners pass each other when running back and forth for hours?

two persons A and B starts from the opposite ends of a $90~\mathrm{km}$ straight track and run to and fro between two ends. Speed of A is $30 ~\mathrm{m}/s$ and B is $\frac{125}{6} ~\mathrm{m/s}$. They continue their motion for 10 hours. How many…
user6595106
  • 91
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the Greatest Number Among $3^{50} ,4^{40} ,5^{30}$ and $6^{20}$

how to find the Greatest Number Among $3^{50} ,4^{40} ,5^{30}$ and $6^{20}$ please give a short cut method
DILIP KUMAR L
  • 57
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Why is my solution wrong?

Question: "Find all x such that ${\frac{x-a}{b}}+{\frac{x-b}{a}}={\frac{b}{x-a}}+{\frac{a}{x-b}}$ , where a and b are constants." My attempt: ${\frac{x-a}{b}}+{\frac{x-b}{a}}={\frac{b}{x-a}}+{\frac{a}{x-b}}$ Let $m=x-a$ ,Let $w=x-b$ .…
user348382
  • 447
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Prove: $||x|-|y||\leq |x+y|$

I have to prove: $||x|-|y||\leq |x+y|\leq |x|+|y|$ I have already proved $|x+y|\leq |x|+|y|$. I saw proofs for $||x|-|y||\leq |x-y|$, can I use the proof for $||x|-|y||\leq |x-y|$ and just add that $|x-y|\leq|x+y|$?
gbox
  • 12,867
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The equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$ has how many solutions?

The equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$ has how many solutions? What would be the correct approach to this problem?Squaring seems to make it even more complicated! P.S:Sorry,at first I wanted to avoid invalid roots.But thanks for your…
user220382
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votes
4 answers

Find the value of k when $f(x) = x^3 -4x^2 + 6x + k$

If $ \ \ a ,b \ \ $and $\ \ c \ \ $ are roots of $ \ \ f(x) = x^3 -4x^2 + 6x + k \ \ $ and $ \frac{1}{a^2 + b^2} + \frac{1}{b^2 + c^2} + \frac{1}{a^2 + c^2} = 1 \ \ \ \ $then find the value of $ \ k $ I have to tell you honestly that I…
ABCDEFG user157844
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8th Grade Algebra Problem I Can't Solve

I have no idea how to solve this. Could anyone give a hand? Thanks! $$2x^{5a} + 6x^{3a} - x^{2a} - 3 = 0$$ PS: I'm guessing this doesn't make sense unless it's also "solve for x" and the equation is = 0, but I'm not certain of that. PPS: My…
Matrym
  • 171
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A tricky but silly doubt regarding the solutions of $x^2/(y-1)^2=1$

Motivation : I have been confused with some degree 2 equation. I suddenly came across a simple equation and couldn't get the quintessence behind that. I have an equation $$\dfrac{x^2}{(y-1)^2}=1 \tag{1}$$ and I was looking for its solutions. It…
IDOK
  • 5,300
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Pythagorean Triplets with "Bounds"

I am interested in the algebraic/geometric way of finding the pythagorean triplets such that $$a^2 + b^2 = c^2$$ $$a + b + c = 1000$$ I do the obvious $$a + b = 1000 - (a^2 + b^2)^{1/2}$$ $$a^2 + b^2 = 1000^2 -2(1000)a - 2(1000)b +2ab + a^2…
Cactus BAMF
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