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Jan
4
comment Given $a+b+c$, Can I calculate $a^2+b^2+c^2$?
No. Are there any more details given? If $ab + bc + ca$ is given, for example, then you can use the relation $(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$.
Nov
3
comment Is zero odd or even?
That is a valid test too. Odd $-$ odd is always even. So zero is even.
Aug
31
comment Find the sum, if exists $\sum\limits_{n=1}^{\infty} \frac{(2n)!}{2^{2n}(n!)^2(n+1)}$
I'd just stick to Shubham's method.
Aug
2
comment What are some good questions for this trick, if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\dots=\alpha$ then $\alpha=\frac{a+c+e+…}{b+d+f+…}$?
Do you happen to have a copy of Higher Algebra by Hall and Knight? It contains quite a few of these in the first chapter.
Jun
26
comment Trigonometry / Finding the exact value
Do you understand that that the cosine function obtains the same value every $2\pi$?
Jun
5
comment How do you solve this using only given values, logarithm rules and no calculator?
You can introduce $\log(2)$ easily. $\log(4) = 2\log(2)= 0.6021 $.
May
22
comment Inequality involving conjugate numerator/denominator pairs
Are you there? Chat is up now.
May
22
comment Inequality involving conjugate numerator/denominator pairs
I would explain the full process to you, but the chat is offline. You can cancel the $x^3$ as a start.
May
20
comment Inequality involving conjugate numerator/denominator pairs
Yes, that's just the wavy-curve method. It's just that you put alternate + and - between the intervals.
May
20
comment Inequality involving conjugate numerator/denominator pairs
Don't worry. Do you know how to solve $(x + 2)(x + 4)(x + 7) < 0$ otherwise, without expanding it into a polynomial?
May
20
comment Inequality involving conjugate numerator/denominator pairs
$(x+2)(x+4)(x+7) < 0$ is another way to say that something is negative. Have you ever used the wavy-curve method?
May
20
comment Inequality involving conjugate numerator/denominator pairs
Corrected it. By the way, you should use the second method.
May
17
comment Absolutet Value Inequality with cases number line
Done! Also included the number line.
May
17
comment Absolutet Value Inequality with cases number line
A number line wouldn't be much of a solution. It can only be used to represent numbers. Depending on different contexts, it's used in different ways. Here, the question might be asking you to use a number line for representing the solution of this inequality.
May
17
comment Absolutet Value Inequality with cases number line
A number? I'm not sure if I perfectly understand your query. Do you mean a number line?
May
17
comment what is the solution for this equation : $2^x-6(2)^{-x}=6$
If $t$ is negative, then $2^x$ will be negative for some real $x$, which is not possible.
Apr
17
comment Trigonometric substitution
Oh, x^2/2 is the angle. OK.
Apr
17
comment Trigonometric substitution
did you mean $\frac{\sin^2(x)}2 = \frac{1}{2}(1 - \cos^2(x))$
Apr
10
comment Proof of a claim on a continuous function in [0,1]
Brian... ${}{}{}$
Mar
1
comment What should be added to $x^4 + 2x^3 - 2x^2 + x - 1$ to make it exactly divisible by $x^2 + 2x - 3$?
@HenningMakholm I'm a ninth grader from the same country as Mayank is, and we are taught polynomial division in the ninth grade.