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Powerful Quadratics

Source: nrich
Find all real solutions to
$$(x^2-7x+11)^{(x^2-11x+30)}=1.$$

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Two Tangents

Source: Reddit
Find a line which is tangent to the curve \(y=x^4-4x^3\) at 2 points.

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A Bit of Spanish

Each of the letters P, O, C, M, U and H represent a different digit from 0 to 9.
Which digit does each letter represent?

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Algebraic Fractions

Given that
$$\frac{3x+y}{x-3y}=-1$$
what is the value of
$$\frac{x+3y}{3x-y}$$
?

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Tags: Algebra

Four Integers

\(a\), \(b\), \(c\) and \(d\) are four positive (and non-zero) integers.
$$abcd+abc+bcd+cda+dab+ab+bc+cd+da+ac+bd\\+a+b+c+d=2009$$
What is the value of \(a+b+c+d\)?

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Times Roamin'

What is the product of this series?
$$(x-a)(x-b)(x-c)...(x-z)$$

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Tags: algebra

x to the Power of x Again

Let \(y=x^{x^{x^{x^{...}}}}\) [\(x\) to the power of (\(x\) to the power of (\(x\) to the power of (\(x\) to the power of ...))) with an infinite number of \(x\)s]. What is \(\frac{dy}{dx}\)?

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x to the Power of x

If \(x^{x^{x^{x^{...}}}}\) [\(x\) to the power of (\(x\) to the power of (\(x\) to the power of (\(x\) to the power of ...))) with an infinite number of \(x\)s] is equal to 2, what is the value of \(x\)?

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