Given that $u = \left(\frac{3}{2}\right)^x$, express $9^x + 6^x = 6(4^x)$ as a quadratic eq

Question

Given that $u = \left(\frac{3}{2}\right)^x$, express $9^x + 6^x = 6(4^x)$ as a quadratic equation in $u$.[3] Hence, or otherwise, solve $9^x + 6^x = 6(4^x)$.[3]

Accepted Answer

(a) $u^2+u-6=0$ (b) $x=\dfrac{\ln 2}{\ln(3/2)}=1.71$ $(3\text{ s.f.})$

2025 DSS PRELIMS P1 Q7

2025 DSS PRELIMS P1 Q7

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