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For the two similar solids, the scalar factor 1:2 means their ratio in
length. Hence, their ratio in volume should be 1^3:2^3 = 1:8.
Now, we have (x-2):(x^2-1) = 1:8,
So, x^2-1 = 8(x-2), or x^2- 8x + 15 = 0.
Factoring (x-3)(x-5) = 0, we have x=3 or 5.