Question

If $P_n=\alpha^n+\beta^n\;, \alpha+\beta=1, \;\alpha \cdot \beta=-1,\;P_{n-1}=11,\; P_{n+1}=29$ Find $(P_n)^2,\;$ where $n\in \mathbb N$

score 132 · Answer 1 · 2026-04-16 23:56:33

132

Views

If $P_n=\alpha^n+\beta^n\;, \alpha+\beta=1, \;\alpha \cdot \beta=-1,\;P_{n-1}=11,\; P_{n+1}=29$ Find $(P_n)^2,\;$ where $n\in \mathbb N$

Published on 16 Apr 2026 - 23:56

score 218 · Answer 2 · 2026-04-13 16:20:19

218

Views

Hessian of quadratic objective function

Published on 13 Apr 2026 - 16:20

score 44 · Answer 3 · 2026-04-13 06:03:42

44

Views

This question is asking about the number of quadratic polynomials possible under given conditions

Published on 13 Apr 2026 - 6:03

score 37 · Answer 4 · 2026-04-13 23:14:46

37

Views

This is question about the integral solutions of 2 different quadratic equations(Question from INMO 1995)

Published on 13 Apr 2026 - 23:14

score 61 · Answer 5 · 2026-04-15 15:15:15

This questions is related to the signs of the coefficients of quadratic polynomials.however doesn't ask about the coefficients themselves.

score 248 · Answer 6 · 2026-04-11 16:09:17

248

Views

Proving that a quadratic equation has no integer solution if c=2n and n is odd

Published on 11 Apr 2026 - 16:09

score 29 · Answer 7 · 2026-04-14 04:06:39

29

Views

Maximum value of f(x) in the given domain according to the given constraints:

Published on 14 Apr 2026 - 4:06

score 53 · Answer 8 · 2026-04-09 22:26:22

53

Views

Mistake in another approach for the old problem

Published on 09 Apr 2026 - 22:26

score 67 · Answer 9 · 2026-04-11 15:16:26

67

Views

How to solve the matrix equation $\mbox{tr}(\mathbf{X}\mathbf{X}^H)\overline{\mathbf{B}}=\mbox{tr}(\mathbf{X}\mathbf{X}^H\mathbf{B})\mathbf{I}$?

Published on 11 Apr 2026 - 15:16

score 53 · Answer 10 · 2026-04-14 18:46:59

53

Views

Why is there a term $3.70074\times 10^{-17}x^2$ in this solution?

Published on 14 Apr 2026 - 18:46

score 57 · Answer 11 · 2026-04-12 05:43:03

57

Views

Show convexity of a quadratic function

Published on 12 Apr 2026 - 5:43

score 117 · Answer 12 · 2026-04-13 19:31:24

117

Views

When is $K = an^2 + bn + c$ a square number?

Published on 13 Apr 2026 - 19:31

score 46 · Answer 13 · 2026-04-16 09:20:01

46

Views

When is $n = \frac{a_{1}x^{2} + a_{2}x + a_{3}}{a_{4}x + a_{5}}$ an integer where $a_{i}$ are incredibly large integers?

Published on 16 Apr 2026 - 9:20

score 89 · Answer 14 · 2026-04-23 11:05:03

89

Views

Rewrite proposition with logical symbols

Published on 23 Apr 2026 - 11:05

score 118 · Answer 15 · 2026-04-13 05:18:55

118

Views

Quadratic formula- calculator gives an answer but cannot do it manually

Published on 13 Apr 2026 - 5:18

List Question

If $P_n=\alpha^n+\beta^n\;, \alpha+\beta=1, \;\alpha \cdot \beta=-1,\;P_{n-1}=11,\; P_{n+1}=29$ Find $(P_n)^2,\;$ where $n\in \mathbb N$

Hessian of quadratic objective function

This question is asking about the number of quadratic polynomials possible under given conditions

This is question about the integral solutions of 2 different quadratic equations(Question from INMO 1995)

This questions is related to the signs of the coefficients of quadratic polynomials.however doesn't ask about the coefficients themselves.

Proving that a quadratic equation has no integer solution if c=2n and n is odd

Maximum value of f(x) in the given domain according to the given constraints:

Mistake in another approach for the old problem

How to solve the matrix equation $\mbox{tr}(\mathbf{X}\mathbf{X}^H)\overline{\mathbf{B}}=\mbox{tr}(\mathbf{X}\mathbf{X}^H\mathbf{B})\mathbf{I}$?

Why is there a term $3.70074\times 10^{-17}x^2$ in this solution?

Show convexity of a quadratic function

When is $K = an^2 + bn + c$ a square number?

When is $n = \frac{a_{1}x^{2} + a_{2}x + a_{3}}{a_{4}x + a_{5}}$ an integer where $a_{i}$ are incredibly large integers?

Rewrite proposition with logical symbols

Quadratic formula- calculator gives an answer but cannot do it manually

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