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UKMT Senior Kangaroo, 2019

Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The real numbers $a$ and $b$ , where $a > b$ , are solutions to the equation $3^{2x} - 10 \times 3^{x+1} + 81 = 0$ . What is the value of $20a^2 + 18b^2$ ?

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