If the Determinant |x−2, 2x−3, 3x−4; 2x−3, 3x−4, 4x−5; 3x−5, 5x−8, 10x−17| = Ax³ + Bx² + Cx + D, Then B + C Is Equal To
JEE Main 2018 PYQ: expand a 3×3 determinant in x as Ax³+Bx²+Cx+D using column operations to create zeros, then find B+C.
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Two Sets A and B Are as Under: A = {(a,b) ∈ R×R : |a−5| < 1 and |b−5| < 1}, B = {(a,b) ∈ R×R : 4(a−6)² + 9(b−5)² ≤ 36}. Then
Set A is an open square defined by |a−5|<1 and |b−5|<1; set B is a filled ellipse. Determine whether A⊂B, B⊂A, or neither, by checking the square's corners against the ellipse.
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α,β Roots of x²−x+1=0 — Find α¹⁰¹+β¹⁰⁷
If α,β are the distinct complex roots of x²−x+1=0, find α¹⁰¹+β¹⁰⁷ by recognising the roots as negatives of cube roots of unity.