Let α, β (α ≠ β) be the values of m, for which the equations x+y+z=1, x+2y+4z=m, and x+4y+10z=m² have infinitely many solutions. Then the value of Σ n=1 ¹⁰ (n^α + n^β) is equal to:

Matrices and Determinants: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q143

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002

Let

\alpha, \beta (\alpha \neq \beta)

be the values of

m

, for which the equations

x+y+z=1

x+2y+4z=m

, and

x+4y+10z=m^2

have infinitely many solutions. Then the value of

\sum_{n=1}^{10} (n^\alpha + n^\beta)

is equal to: