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8h
comment Integer solutions to $\frac{1}{a} + \frac{1}{b} = \frac{1}{12}$.
Related : math.stackexchange.com/questions/1375041/…
10h
comment find $\left( \frac{x}{x+y} \right)^{2007} + \left( \frac{y}{x+y} \right)^{2007}$
@wuiyang, As $r^2+r+1=0$ and $r^3-1=(r-1)(r^2+r+1)$ for finite $r, r^3-1=0$
10h
comment find $\left( \frac{x}{x+y} \right)^{2007} + \left( \frac{y}{x+y} \right)^{2007}$
@wuiyang, I hope not many apart from proofwiki.org/wiki/Exponent_Combination_Laws
11h
comment Find the equation of an equilateral hyperbola passing through a point of a circumference
Why the equation can not be of the form: $$(x-x_0)^2-(y-y_0)^2=a^2$$ See mathworld.wolfram.com/EquilateralHyperbola.html
16h
comment Find a polynomial from an equality
@Nash, Please update your answer with your effort
16h
comment Find a polynomial from an equality
@Nash, If $p(x)=(x-2)(x-4)(ax+b),$ $$(x-8)p(2x)=8(x-1)p(x)$$ leaves $x(4a+b)=0\iff b=-4a$ provided my calculations are right
16h
comment Find a polynomial from an equality
@Nash,I was somehow de-focused in search the highest power. Thanks
16h
comment Find a polynomial from an equality
@Nash, So, we have $$(x-8)(2x-1)(2x-8)(2ax+b)=8(x-1)(x-1)(ax+b)$$ Set $x=8, 1$ one by one
16h
comment Find a polynomial from an equality
@Nash, I just needed to find the coefficients of the highest power(n+1) of $x$, which can not be contributed by the lower terms, right?
16h
comment Counting with potency and simplifing
HINT: $6=2\cdot3, 6^{n+4}=(2\cdot3)^{n+4}=2^{n+4}\cdot3^{n+4}$
18h
comment computing maclaurin series for $(\sin x)^3$ , order $3$
@debi, It's better as it avoids expansion of a multinomial like $$\left[x-\frac{x^3}{3!}+R_{3}(x)\right]^3$$
18h
comment How to show that a curve passes through the origin?
A curve will pass through a given point P$(h,k)$ if $x=h,y=k$ satisfy the given equation of the curve
1d
comment In a triangle, find the minimum and maximum of $\cos(A-B)\cos(B-C)\cos(C-A)$
@LzuTao, "Fix" in other answer should clarify your doubt
1d
comment Finding roots of cubic equation
Use en.wikipedia.org/wiki/Descartes%27_rule_of_signs
1d
comment Find $\lim_{n \to \infty} n[(1+\frac{1}{n})^n - e]$
See math.stackexchange.com/questions/1364171/…
1d
comment Polynomial of 11th degree
@anon, What's that unique choice?
1d
comment Polynomial of 11th degree
@MarianoSuárez-Alvarez, I was pointing to the given condition. But, from that $A$ can assume any arbitrary finite scalar value, right?
1d
comment Polynomial of 11th degree
@MarianoSuárez-Alvarez, See any arbitrary finite constant will satisfy the given condition, right?
2d
comment Wanted: more ways to prove $1+2x+3x^2+\cdots=(1-x)^{-2}$
@daryakhosrotash, See math.stackexchange.com/questions/746388/…
2d
comment Prove that $\alpha + \beta=\frac {\pi}{2}$
How $\cos^2\beta-\sin^2\alpha=\cos(\alpha+\beta)?$