Question

Given the equation $x^2-14x+m=0$, where m is a positive integer. If $p_1,p_2$ are roots, then find the value of $K=(p_1+p_2)^2+2p_1p_2$

score 93 · Answer 1 · 2026-04-15 03:30:07

93

Views

Given the equation $x^2-14x+m=0$, where m is a positive integer. If $p_1,p_2$ are roots, then find the value of $K=(p_1+p_2)^2+2p_1p_2$

Published on 15 Apr 2026 - 3:30

score 973 · Answer 2 · 2026-04-13 20:22:38

973

Views

What is the sum of number of digits of the numbers $2^{2001}$ and $5^{2001}$

Published on 13 Apr 2026 - 20:22

score 38 · Answer 3 · 2026-04-17 05:43:59

Given the functions $f_0,...,f_n$ with $f_0(x)=\frac{1}{x-2}$ and $f_{k+1}(x)=\frac{1}{1-f_k(x)}$ for every $k=0,1,...,n-1$. Evaluate $f_{2000}(2001)$

score 41 · Answer 4 · 2026-04-15 03:26:22

41

Views

The sides of the three squares $ABCD,AEZH$ and $AUIK$ have integer lengths and $(AEZH)-(ABCD)=31$. If $BE=UE$, then calculate $(AUIK)$

Published on 15 Apr 2026 - 3:26

score 103 · Answer 5 · 2026-04-13 21:06:03

103

Views

You have triangle $\triangle ABC$ which is orthogonal $\angle C=90^o$ with circle with center O inscribed in it. Find angle $\angle MCN$

Published on 13 Apr 2026 - 21:06

score 338 · Answer 6 · 2026-04-15 20:41:27

338

Views

Let P denote the product of first n prime numbers (with n > 2). Find all values of $n$ .

Published on 15 Apr 2026 - 20:41

score 42 · Answer 7 · 2026-04-14 09:45:44

42

Views

Given a parabola with equation $y=ax^2+bx+c$ which has as a tip the point $(3, 1)$ and passes through $(2, 0)$. Find out the product $abc$

Published on 14 Apr 2026 - 9:45

score 57 · Answer 8 · 2026-04-15 07:39:56

57

Views

Find the solutions $(x, y)$ of the system $\sqrt{x-y}=x+y-7$ and $\sqrt{x+y}=x-y-1$

Published on 15 Apr 2026 - 7:39

score 77 · Answer 9 · 2026-04-16 15:21:18

77

Views

Given three circles of radius $R$, which touch only at one point and there centers belong to $OD$. Find the length of $AB$.

Published on 16 Apr 2026 - 15:21

score 247 · Answer 10 · 2026-03-25 22:11:06

247

Views

Find the measure of $\angle G$ in a triangle

Published on 25 Mar 2026 - 22:11

score 47 · Answer 11 · 2026-04-14 07:46:56

47

Views

Proof that one of three terms with 3 variables is always smaller or equal to 1

Published on 14 Apr 2026 - 7:46

score 61 · Answer 12 · 2026-04-16 19:52:07

61

Views

$p_1,p_2$ roots of $x^2+3x+5=0$, then the value of the expression $M=\frac{p_1^2+5p_1+7}{p_1^2+7p_1+5}+\frac{p_2^2+5p_2+7}{p_2^2+7p_2+5}$

Published on 16 Apr 2026 - 19:52

score 56 · Answer 13 · 2026-04-15 18:25:22

56

Views

$S = \{A \in \mathcal{M}_{2x2} \colon A^2 = -I_2\}$, find elements in the set such that...

Published on 15 Apr 2026 - 18:25

score 247 · Answer 14 · 2026-04-15 19:03:13

247

Views

Prove that $(I_n-A)^{-1}$ exists

Published on 15 Apr 2026 - 19:03

score 109 · Answer 15 · 2026-04-15 20:19:53

109

Views

Find the determinant of a "piecewise" matrix

Published on 15 Apr 2026 - 20:19

List Question

Given the equation $x^2-14x+m=0$, where m is a positive integer. If $p_1,p_2$ are roots, then find the value of $K=(p_1+p_2)^2+2p_1p_2$

What is the sum of number of digits of the numbers $2^{2001}$ and $5^{2001}$

Given the functions $f_0,...,f_n$ with $f_0(x)=\frac{1}{x-2}$ and $f_{k+1}(x)=\frac{1}{1-f_k(x)}$ for every $k=0,1,...,n-1$. Evaluate $f_{2000}(2001)$

The sides of the three squares $ABCD,AEZH$ and $AUIK$ have integer lengths and $(AEZH)-(ABCD)=31$. If $BE=UE$, then calculate $(AUIK)$

You have triangle $\triangle ABC$ which is orthogonal $\angle C=90^o$ with circle with center O inscribed in it. Find angle $\angle MCN$

Let P denote the product of first n prime numbers (with n > 2). Find all values of $n$ .

Given a parabola with equation $y=ax^2+bx+c$ which has as a tip the point $(3, 1)$ and passes through $(2, 0)$. Find out the product $abc$

Find the solutions $(x, y)$ of the system $\sqrt{x-y}=x+y-7$ and $\sqrt{x+y}=x-y-1$

Given three circles of radius $R$, which touch only at one point and there centers belong to $OD$. Find the length of $AB$.

Find the measure of $\angle G$ in a triangle

Proof that one of three terms with 3 variables is always smaller or equal to 1

$p_1,p_2$ roots of $x^2+3x+5=0$, then the value of the expression $M=\frac{p_1^2+5p_1+7}{p_1^2+7p_1+5}+\frac{p_2^2+5p_2+7}{p_2^2+7p_2+5}$

$S = \{A \in \mathcal{M}_{2x2} \colon A^2 = -I_2\}$, find elements in the set such that...

Prove that $(I_n-A)^{-1}$ exists

Find the determinant of a "piecewise" matrix

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