Competition problem — Algebra — Maths Olympiad Prep

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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. Spacing and $ signs are ignored.

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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