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, 2012

Algebra Difficulty 1.4 Junior Find the answer Canada

The operation $\nabla$ is defined by $g \nabla h = g^2-h^2$ . For example, $2\nabla 1 = 2^2-1^2=3$ .If $g>0$ and $g \nabla 6 = 45$ , the value of $g$ is

Pick one

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 $g = \sqrt{81}=9$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.