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3(x−2)×((x+1)(x)(x−1)2)=204123^{(x-2)}\times\left(\frac{(x+1)(x)(x-1)}{2}\right)=20412

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Full solution

Q. 3(x−2)×((x+1)(x)(x−1)2)=204123^{(x-2)}\times\left(\frac{(x+1)(x)(x-1)}{2}\right)=20412
  1. Rewrite Equation: Rewrite the equation to make it clearer.\newline\(3^{(x−2-2)}\times\left(\frac{(x+11)(x)(x−1-1)}{22}\right)=2041220412
  2. Simplify Quadratic Expression: Simplify the quadratic expression. (x+1)(x)(x−1)=x(x2−1)(x+1)(x)(x-1) = x(x^2-1)
  3. Substitute Simplified Expression: Substitute the simplified expression back into the equation. 3(x−2)×(x(x2−1)2)=204123^{(x-2)}\times\left(\frac{x(x^2-1)}{2}\right)=20412
  4. Multiply by 22: Multiply both sides by 22 to get rid of the fraction.\newline3(x−2)×x(x2−1)=408243^{(x-2)}\times x(x^2-1)=40824
  5. Divide to Isolate Term: Divide both sides by xx to isolate the exponential term.\newline3(x−2)(x2−1)=40824x3^{(x-2)}(x^2-1)=\frac{40824}{x}
  6. Correct Mistake: Realize there's a mistake in the previous step; we can't divide by xx as it's part of the term x2−1x^2-1. Go back to the previous step.

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