Powerful Quadratics

This comes in two parts, with the first being less fiendish than the second. It’s great for practising both quadratics and laws of indices, and you can get a lot from making sure that you find all the solutions. For a real challenge (requiring a bit more knowledge), you could consider finding the complex solutions.
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Powerful Quadratics


This resource is from Underground Mathematics.

 

 



(i) Find all real solutions of the equation

$$(x^2−7x+11)^{(x^2−11x+30)}=1.$$

(ii) Find all real solutions of the equation

$$(2−x^2)^{(x^2−3\sqrt{2}x+4)}=1.$$

 

 

 

This is an Underground Mathematics resource.

Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.

Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.