Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 4"

Revision as of 00:20, 11 July 2021

If $\frac{x+2}{6}$ is its own reciprocal, find the product of all possible values of $x.$

From the problem, we know that $\frac{x+2}{6} = \frac{6}{x+2}$ $(x+2)^2 = 6^2$ $x^2+ 4x + 4 = 36$ $x^2 + 4x - 32 = 0$ $(x-8)(x+4) = 0$

Thus, $x = 8$ or $x = -4$ . Our answer is $8 \cdot(-4)=\boxed{-32}$

~Bradygho

$\frac{x+2}{6}=\frac{6}{x+2} \implies x^2+4x-32$ Therefore, the product of the root is $-32$ ~ kante314

Revision as of 22:09, 10 July 2021 (view source) Bradygho (talk \| contribs) (→‎Solution) ← Older edit		Revision as of 00:20, 11 July 2021 (view source) Kante314 (talk \| contribs) (→‎Solution) Newer edit →
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		+	<math>\frac{x+2}{6}=\frac{6}{x+2} \implies x^2+4x-32</math> Therefore, the product of the root is <math>-32</math> ~ kante314