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Question

The total number of distinct xR for which
∣ ∣ ∣xx21+x32x4x21+8x33x9x21+27x3∣ ∣ ∣=10 is

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Solution

x.x2∣ ∣ ∣111+x3241+8x3391+27x3∣ ∣ ∣=10x3∣ ∣111241391∣ ∣+x6∣ ∣1112483927∣ ∣=10x3∣ ∣001131281∣ ∣+x6∣ ∣1002263624∣ ∣=10x3(86)+x6(4836)=106x6+x35=0(6x35)(x3+1)=0x3=56,x3=1x=(56)13,x=1Two distinct value

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