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Simplify: x(1xx3)−xx−2x=0 x(\frac{1}{x\sqrt{x^3}})-x^x-\frac{2}{x}=0\

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Full solution

Q. Simplify: x(1xx3)−xx−2x=0 x(\frac{1}{x\sqrt{x^3}})-x^x-\frac{2}{x}=0\
  1. Simplify Term: Simplify the term x(1/xx3)x(1/x\sqrt{x^3}).\newlineCalculation: x(1/xx3)=x×(1/x×x3/2)=x1−1+3/2=x3/2x(1/x\sqrt{x^3}) = x \times (1/x \times x^{3/2}) = x^{1 - 1 + 3/2} = x^{3/2}.
  2. Rewrite Equation: Rewrite the equation using the simplified term.\newlineCalculation: x32−xx−2x=0x^{\frac{3}{2}} - x^x - \frac{2}{x} = 0.
  3. Isolate x Terms: Attempt to isolate x terms.\newlineCalculation: x(3/2)−xx=2xx^{(3/2)} - x^x = \frac{2}{x}.
  4. Clear Fraction: Multiply through by xx to clear the fraction.\newlineCalculation: x×(x32−xx)=x×(2x),x52−xx+1=2x \times (x^{\frac{3}{2}} - x^x) = x \times (\frac{2}{x}), x^{\frac{5}{2}} - x^{x+1} = 2.

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