Question

Solve the equation $5x^2+5y^2-8xy-2x-4y+5=0$

score 834 · Answer 1 · 2016-12-16 14:36:49

834

Views

Solve the equation $5x^2+5y^2-8xy-2x-4y+5=0$

Published on 16 Dec 2016 - 14:36

score 92 · Answer 2 · 2016-12-16 19:54:40

92

Views

Is my result to $z^2 - (3+4i)z - 1 + 7i = 0$ right?

Published on 16 Dec 2016 - 19:54

score 182 · Answer 3 · 2016-12-16 20:20:26

182

Views

How can the equation be positive in the interval $ -1 < x < \frac{7-\sqrt{73}}{2}$?

Published on 16 Dec 2016 - 20:20

score 466 · Answer 4 · 2026-04-01 03:10:05

466

Views

Prove that $\frac{a}{2}x^2+bx+c=0$ has a root between $x_1$ and $x_2$.

Published on 01 Apr 2026 - 3:10

score 82 · Answer 5 · 2026-03-26 07:58:35

82

Views

Can $ x^2+\frac{x^2}{(x+1)^2}=3 $ be solved by 'completing square method'?

Published on 26 Mar 2026 - 7:58

score 35 · Answer 6 · 2016-12-17 17:27:42

35

Views

Solving the system of equations

Published on 17 Dec 2016 - 17:27

score 185 · Answer 7 · 2016-12-18 08:02:36

If $3x^2+2\alpha xy+2y^2+2ax-4y+1$ can be resolved into two linear factors, prove that $\alpha$ is the root of the equation $x^2+4ax+2a^2+6=0$.

score 630 · Answer 8 · 2016-12-18 08:29:11

630

Views

If $P(x)=ax^2+bx+c$ and $Q(x)=-ax^2+dx+c$, $ac$is not $0$, then prove that $P(x)\cdot Q(x)=0$ has at least 2 real roots.

Published on 18 Dec 2016 - 8:29

score 110 · Answer 9 · 2026-04-04 03:18:17

110

Views

How to factorize $a^2-b^2-a+b+(a+b-1)^2$?

Published on 04 Apr 2026 - 3:18

score 59 · Answer 10 · 2026-04-04 03:24:45

59

Views

How to factor $a^2(a+1/a)^2-4a^2(a+1/a)+4a^2$ to get $(a-1)^4$?

Published on 04 Apr 2026 - 3:24

score 136 · Answer 11 · 2026-03-31 23:29:22

136

Views

How to find the smallest n for inequality involving factorial, $n! > 10^6 $, what is $n$?

Published on 31 Mar 2026 - 23:29

score 87 · Answer 12 · 2026-03-31 21:02:57

87

Views

Showing $\lvert \frac{x^2-2x+3}{x^2-4x+3}\rvert\le1\Rightarrow x\le0$

Published on 31 Mar 2026 - 21:02

score 1.4k · Answer 13 · 2026-04-03 23:46:36

1.4k

Views

Determine $x,y,z ∈ R$ such that $2x^2+y^2+2z^2-8x+2y-2xy+2xz-16z+35=0$

Published on 03 Apr 2026 - 23:46

score 3.3k · Answer 14 · 2016-12-19 12:25:08

Find the interval in which $m$ lies so that the expression $\frac{mx^2+3x-4}{-4x^2+3x+m}$ can take all real values, $x$ being real

score 93 · Answer 15 · 2016-12-20 00:20:18

93

Views

How do you solve $y=ax^2-ax+b$ for $x$?

Published on 20 Dec 2016 - 0:20

List Question

Solve the equation $5x^2+5y^2-8xy-2x-4y+5=0$

Is my result to $z^2 - (3+4i)z - 1 + 7i = 0$ right?

How can the equation be positive in the interval $ -1 < x < \frac{7-\sqrt{73}}{2}$?

Prove that $\frac{a}{2}x^2+bx+c=0$ has a root between $x_1$ and $x_2$.

Can $ x^2+\frac{x^2}{(x+1)^2}=3 $ be solved by 'completing square method'?

Solving the system of equations

If $3x^2+2\alpha xy+2y^2+2ax-4y+1$ can be resolved into two linear factors, prove that $\alpha$ is the root of the equation $x^2+4ax+2a^2+6=0$.

If $P(x)=ax^2+bx+c$ and $Q(x)=-ax^2+dx+c$, $ac$is not $0$, then prove that $P(x)\cdot Q(x)=0$ has at least 2 real roots.

How to factorize $a^2-b^2-a+b+(a+b-1)^2$?

How to factor $a^2(a+1/a)^2-4a^2(a+1/a)+4a^2$ to get $(a-1)^4$?

How to find the smallest n for inequality involving factorial, $n! > 10^6 $, what is $n$?

Showing $\lvert \frac{x^2-2x+3}{x^2-4x+3}\rvert\le1\Rightarrow x\le0$

Determine $x,y,z ∈ R$ such that $2x^2+y^2+2z^2-8x+2y-2xy+2xz-16z+35=0$

Find the interval in which $m$ lies so that the expression $\frac{mx^2+3x-4}{-4x^2+3x+m}$ can take all real values, $x$ being real

How do you solve $y=ax^2-ax+b$ for $x$?

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