CEMC Pascal

Algebra Difficulty 1.8 Junior Find the answer

The operation $\nabla$ is defined by $g \nabla h=g^{2}-h^{2}$ . If $g>0$ and $g \nabla 6=45$ , what is the value of $g$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Using the definition of the operation, $g \nabla 6=45$ gives $g^{2}-6^{2}=45$ . Thus, $g^{2}=45+36=81$ . Since $g>0$ , then $g=\sqrt{81}=9$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.