In the compound \( \text{MnO}_4^- \), the oxidation state of manganese (Mn) is +7. When \( \text{MnO}_4^- \) is reduced to \( \text{Mn}^{2+} \), the oxidation state of manganese decreases to +2.
This is a reduction process, as the manganese atom gains electrons, reducing its oxidation state.
If \[ f(x) = \int \frac{1}{x^{1/4} (1 + x^{1/4})} \, dx, \quad f(0) = -6 \], then f(1) is equal to:
If the system of equations \[ (\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 \] \[ \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 \] \[ (\lambda + 1)x + (\lambda + 2)y - (\lambda + 2)z = 9 \] has infinitely many solutions, then \( \lambda^2 + \lambda \) is equal to: