Quadratic equations

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Favourite

Power Quady

Age

16 to 18

Challenge level

Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.
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Square Mean

Age

14 to 16

Challenge level

Is the mean of the squares of two numbers greater than, or less than, the square of their means?
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How Old Am I?

Age

14 to 16

Challenge level

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
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Favourite

Quadratic Patterns

Age

14 to 16

Challenge level

Surprising numerical patterns can be explained using algebra and diagrams...
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Favourite

Interactive Number Patterns

Age

14 to 16

Challenge level

How good are you at finding the formula for a number pattern ?
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Favourite

Golden Thoughts

Age

14 to 16

Challenge level

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
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Favourite

Partly Circles

Age

14 to 16

Challenge level

What is the same and what is different about these circle questions? What connections can you make?
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Favourite

Mega Quadratic Equations

Age

14 to 18

Challenge level

What do you get when you raise a quadratic to the power of a quadratic?
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Favourite

Always Two

Age

14 to 18

Challenge level

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
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Favourite

In Between

Age

16 to 18

Challenge level

Can you find the solution to this algebraic inequality?