All Questions ⁺⁰237243 Questions

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Algebra

Let x and y be positive real numbers. If x + y = 1, then find the maximum value of xy + y^3.

AnswerscorrectIy Mar 18, 2025

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+1208

Algebra

Find the minimum value of
\frac{x^2}{x + 2}
for x > 2.

AnswerscorrectIy Mar 18, 2025

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+1208

Algebra

Find the minimum value of the product
P(x,y,z) = (2x + 3y)(x + 4z) \left( y + \frac{5}{3} z \right),
when xyz = 1, and x, y, z are positive real numbers.

AnswerscorrectIy Mar 18, 2025

Mar 17, 2025

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+116

Algebra

Find the maximum p such that
2x^4 y^2 + \frac{9}{4} y^4 z^2 + \frac{3}{4} z^4 x^2 + 3x^3 y^3 + 10x^3 z^3 + 15y^3 z^3 - px^2 y^2 z^2
is always nonnegative for all real x, y, and z.

coIinqiu Mar 17, 2025

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+116

Inequality

Let w, x, y, and z be positive real numbers. If w + 2x + 3y + 6z = 8 - w^2 - x^2 - y^2 - z^2, then what is the maximum value of wxyz?

coIinqiu Mar 17, 2025

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+141

Super Confusing Math Problem ( Read Description )

PLEASE READ DESCRIPTION BEFORE ANSWERING
I first picked option A because thats what I think was right and AI and even google was saying its correct... but it ended up being wrong so then I picked option C. because that was my next bet read more ..

acyclics Mar 17, 2025

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+1208

Algebra

Let a and b be positive real numbers. Find the minimum value of
(a + b) \left( \frac{1}{a + 1} + \frac{1}{b + 1} \right)

AnswerscorrectIy Mar 17, 2025

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+1208

Algebra

Fill in the blanks, to make a true equation.
3/(3^2 - 1) + 3^2/(3^4 - 1) + 3^3/(3^6 - 1) + 3^4/(3^8 - 1) + ... + 3^(2(n - 1))/(3^(2n) - 1) = ___/___
Hint: Let S_n = \frac{3}{3^2 - 1} + \frac{3^2}{3^4 - 1} + \frac{3^3}{3^6 - 1} read more ..

AnswerscorrectIy Mar 17, 2025

Mar 16, 2025

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+1208

Algebra

Find the number of points of intersection between the graphs of the following equations: \begin{align*}
y = |2x + 5|,
y = -|3x - 2| + |4x - 7| + x.

AnswerscorrectIy Mar 16, 2025

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+1208

Algebra

Let x be a positive real number. Show that
\frac{1}{x} \ge 3 - 2x
Describe when we have equality.

AnswerscorrectIy Mar 16, 2025

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+1208

Algebra

Let
f(x) = \frac{x^4 + 2x^3 + 3x^2 + 2x + 1}{x}.
Find the minimum value of x for x > 0.

AnswerscorrectIy Mar 16, 2025

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+1208

Algebra

Let $x$ and $y$ be real numbers such that
x^2 + 3xy + 2y^2 = 1 - 12x + 5y.
Find all possible values of x + y. Enter your answer using interval notation.

AnswerscorrectIy Mar 16, 2025

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+1208

Algebra

Let a and b be real numbers such that
(a^2 + 1)(b^2 + 4) = 14ab + 21.
Find the largest possible value of a^2 + b^2.

AnswerscorrectIy Mar 16, 2025

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+1208

Algebra

Let x and y be real numbers satisfying
\frac{x^2y^2 - 1}{2y - 1} = 4x + y.
Find the largest possible value of x.

AnswerscorrectIy Mar 16, 2025

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+1208

Algebra

Let x and y be real numbers. Find the maximum value of $(x + y)^2$, if $x$ and $y$ satisfy $x^2 + y^2 = 5 + 2xy$.

AnswerscorrectIy Mar 16, 2025

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+1208

Algebra

Find the maximum value of f(a), where a is a positive integer, and
f(x) = \frac{13 + x}{2x + 7 - x^2}.

AnswerscorrectIy Mar 16, 2025

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+1208

Algebra

Compute
\sum_{k = 1}^{100} k (\lceil \log_3 k \rceil - \lfloor \log_9 k \rfloor).

AnswerscorrectIy Mar 16, 2025

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+1208

Algebra

Find the smallest positive real number x such that
\lfloor x^2 \rfloor - x \lfloor x \rfloor = \lfloor x^3 \rlfoor/x

AnswerscorrectIy Mar 16, 2025

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+1208

Algebra

Find all x for which
\Big| x - |x - 2| \Big| = \lfloor x \rfloor + \lfloor 2x \rfloor
Express your answer in interval notation.

AnswerscorrectIy Mar 16, 2025

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