siIviajendeukie

153 Questions
13 Answers

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Algebra

Let $a$ be a real number such that a - \frac{1}{a} = 4 + a + \frac{1}{a} Compute $a^3 - \frac{1}{a^3}$.

siIviajendeukie 03.11.2024

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Algebra

Let
f(x) = \sqrt[3]{x + \sqrt[3]{x}}
Find the largest three-digit value of $x$ such that $f(x)$ is an integer.

siIviajendeukie 03.11.2024

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Complex Numbers

Let $x$ and $y$ be complex numbers. If $x + y =2$ and $xy = 5 - x^2 + xy - y^2$, then what is $x^2 + y^2$?

siIviajendeukie 02.11.2024

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Algebra

Compute
1 + \frac{3}{7} + \frac{5}{7^2} + \frac{7}{7^3}

siIviajendeukie 02.11.2024

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Algebra

Compute
1 + \frac{3}{4} + \frac{5}{4^2} + \frac{7}{4^3}

siIviajendeukie 02.11.2024

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Algebra

A geometric sequence has 400 terms. The first term is 1600 and the common ratio is $-\frac{1}{2}.$ How many terms of this sequence are greater than 1000?

siIviajendeukie 02.11.2024

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Algebra

Find all c such that |c + 5| - 3c = 10 - 5|c - 1| + 7|c + 8|.

siIviajendeukie 02.11.2024

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Algebra

Assume that $f(3) = 4$. Name a point that must be on the graph of y= f(2/5*x + 4) + f(3x - 1) .

siIviajendeukie 02.11.2024

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Algebra

Let a(x) and b(x) be functions. Find (a\circ b)(3) - (b\circ a)(3) if $a(x) = 2x + 5$ and $b(x) = 4 - x^2$.

siIviajendeukie 02.11.2024

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Number Theory

Find the largest positive integer n for which there exist positive integers a, b, and c such that
\gcd(a + 3b, b + 3c, c + 3a) = nabc

siIviajendeukie 29.10.2024

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Number Theory

Let N be the number of ordered 6-tuples (a_1, a_2, a_3, a_4, a_5, a_6) of positive integers that satisfy
\frac{1}{a_1} + \frac{1}{a_2} + \frac{1}{a_3} + \frac{1}{a_4} + \frac{1}{a_5} + \frac{1}{a_6} = 6.
Find the remainder when N is divided mehr ..

siIviajendeukie 29.10.2024

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Number Theory

Let a, b, and c be integers such that 7a + 4b = 3c. Find the largest integer that always divides $abc$.

siIviajendeukie 29.10.2024

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Algebra

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 mehr ..

siIviajendeukie 21.10.2024