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Results tagged with algebra-precalculus
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user 1104251
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.
2
votes
2
answers
117
views
Let $x, y\in \mathbb{R}$, solve the following system: $\begin{cases}x^9+y^9=1\\x^{10}+y^{10}...
Let $x, y\in \mathbb{R}$, solve the following system: $$\begin{cases}x^9+y^9=1\\x^{10}+y^{10}=1 \end{cases}$$
I have tried to use notations, $S = x+y$ and $P=xy$, but I couldn't continue because of t …
- 301
7
votes
4
answers
246
views
Prove that the equation $x^4-4x^3-14x^2-4x+1=0$ has a root $x = \tan 9^\circ$
Prove that the equation $x^4-4x^3-14x^2-4x+1=0$ has a root $x = \tan 9^\circ$. I have tried calculating $\tan 9^\circ$ and substituting it in the equation but it is pretty tough to calculate that. Can …
- 301
0
votes
1
answer
70
views
Find the maximum value of $|b|+|c|$.
Let $\mathit{f}:\mathbb{R}\to\mathbb{R}$, $\mathit{f}(x)=ax^2+bx+c$ such that $|\mathit{f}(x)|\le1$ for any $x\in\mathbb{R}$ with $|x|\le1$. Find the maximum value of $|b|+|c|$. I presume that if $x=0 …
- 301
1
vote
1
answer
42
views
Given any $a,b,c \geq 1$, prove that $a^2 + b^2 + c^2 \geq 2a\sqrt{b-1} + 2b\sqrt{c-1} + 2c\...
Given any $a,b,c \geq 1$, prove that:
$a^2 + b^2 + c^2 \geq 2a\sqrt{b-1} + 2b\sqrt{c-1} + 2c\sqrt{a-1}$
I tried using most of the popular inequalities and I didn't end up anywhere. Can anyone guide me …
- 301