# 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.

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### Is there an exact answer to this problem?

enter to see the problem To translated from Thai English as I could If y is a real number that satifies y^{5} + y - 1 = 0 then find y^{3} + y^{2} +1 I tried to solve it by substitution but still can'...
1 vote
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### Inscribing two circles and an ellipse in a square

A square of given side length $S$ is to inscribe two circles and an ellipse as shown in the figure below. If the radius of circle $(1)$ is given, determine the center and radius of circle $(2)$, then ...
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1 vote
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### Nit picking at whether these two functions are the same

I have a simple and dumb question: are these two functions the same? $$f(x)=x$$ and $$g(x)=\frac{x^2}{x}$$ Obviously f and g are the same since you can simplify by x but are they really? $f$ is ...
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### Is it possible to calculate power of binary number like $a^b$ where $a$ is binary number and $b$ is decimal number?

Is it possible to calculate power of binary number like $a^b$ where $a$ is binary number and $b$ is decimal number? I mean, is there a formula for it?
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### If $9^{x+1} + (a^2 - 4a - 2)3^x + 1> 0$ for all $x ∈ R$, then which of the following is true?

If $9^{x+1} + (a^2 - 4a - 2)3^x + 1> 0$ for all $x ∈ R$, then which of the following is true? The options given are as follows : a) $a ∈ R$ b) $a ∈ R^+$ c) $a ∈ [1,∞)$ d) $a ∈ R -$ {2} The answer ...
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### $x=p+\frac{1}{p}$ , $y=q+\frac{1}{q}$ and $z=\frac{p}{q}+\frac{q}{p}$. Then find the value of $x^2+y^2+z^2-xyz$. [closed]

$x=p+\frac{1}{p}$ , $y=q+\frac{1}{q}$ and $z=\frac{p}{q}+\frac{q}{p}$. Then find the value of $x^2+y^2+z^2-xyz$. In this question I have found the answer by putting random values of p and q directly. ...
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### Conversion of a result number to a specified unit of measure

It's a very simple question, but I need to know how to convert numbers, because in several cases I ran into this topic and felt unsure about this. So for example we're counting a unit measure of time, ...
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### Difficult algebra problem related to finding a specific value in terms of "$c$" or "$b$"

If $\frac{a}{b}=\frac{b}{c}=\frac{c}{a}$ and $ax^2+bx+c=0$ then the value of $b^2x^4+b^2c^2x^2+2b^2cx^3$ is A) $c^4$ $\quad$B) $-c$ $\quad$C) $-c^2$ $\quad$D) $b^4$ Can anyone please help me with this ...
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### Suppose that $-1\leq ax^2 + bx + c\leq 1$ for $-1\leq x\leq 1$, where $a, b$ and $c$ are real numbers, prove that $-4\leq 2ax + b\leq 4$. [duplicate]

I see that for $x = 0, |c|\leq 1$, for $x = -1, |a - b + c|\leq 1$ and for $x = 1, |a + b + c|\leq 1$. Thus, $|2a + 2c|\leq 2\Rightarrow |2a|< 4$ and $|b|\leq 1$. This, gives me $|2a + b|\leq 5$, ...
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1 vote
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### In an isosceles triangle with base $a$ and congruent side $b$ the vertex angle is equal to $20°$. Prove that $a^3 + b^3 = 3ab^2$.

I was trying to solve this problem: In an isosceles triangle with base $a$ and congruent side $b$ the vertex angle is equal to $20°$. Prove that $a^3 + b^3 = 3ab^2$. After a long time of thinking ...
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