Questions asked by George C.
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#x^410x^2+1=0# has one root #x=sqrt(2)+sqrt(3)#. What are the other three roots and why?

The function #f(x) = 1/(1x)# on #RR# \ #{0, 1}# has the (rather nice) property that #f(f(f(x))) = x#. Is there a simple example of a function #g(x)# such that #g(g(g(g(x)))) = x# but #g(g(x)) != x#?

If you are told that #x^73x^5+x^44x^2+4x+4 = 0# has at least one repeated root, how might you solve it algebraically?

How can we graph the sawtooth function #x  floor(x)#?

If #z in CC# then what is #sqrt(z^2)#?

Given an integer #n# is there an efficient way to find integers #p, q# such that #abs(p^2n q^2) <= 1# ?

How do you prove that the set of roots of polynomial equations in one variable with integer coefficients is algebraically closed?

What mathematical conjecture do you know of that is the easiest to explain, but the hardest to attempt a proof of?

How do you show that if #n# is a nonzero integer then #(4/5+3/5i)^n != 1# ?

What simple rigorous ways are there to incorporate infinitesimals into the number system and are they then useful for basic Calculus?

How do you find the zeros of #5x^8+4x^7+20x^5+42x^4+20x^3+4x+5# algebraically?

If the zeros of #x^5+4x+2# are #omega_1#, #omega_2#,.., #omega_5#, then what is #int 1/(x^5+4x+2) dx# ?

What are the zeros of #x^38x4#?

What does cutting squares from an A4 (#297"mm"xx210"mm"#) sheet of paper tell you about #sqrt(2)#?

For what integer values of #k# does #sqrt(x)+sqrt(x+1)=k# have a rational solution?

The sequence #0, 2, 8, 30, 112, 418,...# is defined recursively by #a_0 = 0#, #a_1 = 2#, #a_(n+1) = 4a_na_(n1)#. What is the formula for a general term #a_n#?

If all you know is rational numbers, what is the square root of #2# and how can you do arithmetic with it?

How do you factor completely #f(x) = x^52 i x^4(5+3 i) x^3(73 i) x^2+(6+11 i) x(1+3 i)# ?

How do you find the discriminant of #x^73x^5+x^44x^2+4x+4# and what does it tell us?

What are the roots of #8x^37x^261x+6=0# ?

Why does it make sense to define #sqrt(1) = i# but not to define #i = sqrt(1)# ?

Does this word construction (a meditation on Exodus 3) count as poetry, and if so how would you classify it?

Given #f(x) = x^33x#, how can you construct an infinitely differentiable oneone function #g(x):RR>RR# with #g(x) = f(x)# in #(oo, 2] uu [2, oo)#?

Apart from #2, 3# and #3, 5# is there any pair of consecutive Fibonacci numbers which are both prime?

How do you find the zeros of #f(x) = 2x^3+2x^22x1# ?

What are the zeros of #f(x) = x^3140x^2+7984x107584#?

A friend chooses two #5# digit positive integers with no common factors and divides one by the other, telling you the result to #12# significant digits. How can you find out what the two numbers were?

If #f(x) = x^5+px+q# (Bring Jerrard normal form) with #p, q# integers, then what are the possible natures of the zeros?

How do you find a #2xx2# matrix #A# with rational coefficients such that #A^2+A+((1,0),(0,1)) = ((0,0),(0,0))# ?

If one of the roots of #x^33x+1=0# is given by the rational (companion) matrix #((0,0,1),(1,0,3),(0,1,0))#, then what rational(?) matrices represent the other two roots?

If #kappa = cos((2pi)/9)+i sin((2pi)/9)# (i.e. the primitive Complex #9#th root of #1#) then how do you express #kappa^8# in the form #a+b kappa + c kappa^2 + d kappa^3 + e kappa^4 + f kappa^5# where #a, b, c, d, e, f# are rational?

Would it be possible to enhance the search facility to find answers within subjects, with particular participants, etc.?

Are octonions numbers?

How can you define a function with domain the whole of #RR# and range the whole of #CC#?

If #a# and #b# are nonzero integers, is it possible for #x^3ax^2+(a^2b)x+a(2ba^2)=0# to have more than one Real root?

What are the roots of #x^3+52x^2+1060x4624 = 0#?

If #M = ((0,0,0,0,2),(1,0,0,0,4),(0,1,0,0,0),(0,0,1,0,0),(0,0,0,1,0))# and #A# is an invertible rational #5xx5# matrix which commutes with #M#, then is #A# necessarily expressible as #A = aM^4+bM^3+cM^2+dM+e# for some scalar factors #a, b, c, d, e#?

How do you prove that #sum_(n=1)^oo (n^(1/n)1)# diverges?

If #M = ((0,0,1),(1,0,1),(0,1,0))# and #A# is an invertible rational #3xx3# matrix which commutes with #M#, then is #A# necessarily expressible as #A = aM^2+bM+cI_3# for some scalar factors #a, b, c#?

Given a function #h# defined by #h(x) = (x4)/(x+4)#, how do you find a function #f# such that #h = f@f# ?

Is there a rational number #x# such that #sqrt(x)# is irrational, but #sqrt(x)^sqrt(x)# is rational?

What fun, useful, mathematical fact do you know that is not normally taught at school?

Are there equivalent expressions for "eagleeyed" for senses other than sight?

What possible values can the difference of squares of two Gaussian integers take?

Would it be possible to see how many times an answer has been viewed by other people?

How can we attempt to simplify expressions of the form #sqrt(p+qsqrt(r))# where #p, q, r# are rational?

How can you prove that #1/(0!)+1/(1!)(n1)+1/(2!)(n1)(n2)+1/(3!)(n1)(n2)(n3)+... = 2^(n1)# ?

What are the zeros of #x^426x^2+1# ?

How do you derive exact algebraic formulae for #sin (pi/10)# and #cos (pi/10)# ?

How do you factor #x^5y^5#?

What are the zeros of #7x^3+70x^2+84x+8=0# ?

Would it be helpful to have some kind of Advanced Algebra subject classification?

Can you find the cube root of a positive integer using a recursively defined sequence?

Which two consecutive integers are such that the smaller added to the square of the larger is #21#?

There does not seem to be a suitable graphic for Algebra level 26 or higher. Should there be?

What is the area of a triangle with vertices #(x_1, y_1)#, #(x_2, y_2)#, #(x_3, y_3)# ?

Would the Lagrange points L4 and L5 of the SunEarth system make good locations for a pair of telescopes or does the likely debris around them present a hazard that outweighs the potential advantages?

"Unanswered" filter is cleared on returning to list. Can it be made sticky?

Given a monic cubic function #x^3+bx^2+cx+d# with zeros #alpha, beta, gamma# how can you construct a set of #6xx6# rational matrices that form a field isomorphic to #QQ[alpha, beta, gamma]# ?

How do you simplify #root(3)(135+78sqrt(3))+root(3)(13578sqrt(3))# ?

What different numbers might be considered conjugates of #1+(root(3)(2))i# and why?