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Your LHS in the 'RTP' line is not always less than 2.5. E.g. in an equilateral triangle, all angles are 60º, and cos(60º) = ½, so your LHS is then 2•(½ + ½ + ½) = 3.
I realised that and was trying to look for which line was wrong.Your LHS in the 'RTP' line is not always less than 2.5. E.g. in an equilateral triangle, all angles are 60º, and cos(60º) = ½, so your LHS is then 2•(½ + ½ + ½) = 3.
It still says LHS ≤ 2.5 on the second last line (this could just be a typo, I haven't read through the proof, just skimmed it).I realised that and was trying to look for which line was wrong.
It has been found.It was a dumb error in failing to carry a constant of 2 through on some terms.
View attachment 32240
nvmI realised that and was trying to look for which line was wrong.
It has been found.It was a dumb error in failing to carry a constant of 2 through on some terms.
View attachment 32240
Knowing the angles of a triangle isn't enough to determine a unique area, since the triangles could have different sizes for given angles (they would all be similar triangles).Can I post a question:
Needs fixing just wait...
You may assume or derive a suitable formula for the area of a triangle in terms of the sides or angles.
I'll rewrite it in latex for you:Show that 4m^2+17n^2 and 4n^2+17m^2 cannot be both be perfect squares, where n, and m are positive integers
by letting each of the expressions equal to u^2 and v^2 respectively, we can deduce that m and n must both be odd for u and v to be integers. Hence, we only consider the case where m and n areboth odd integers. But this is a contradiction as for each expression, upon division by 8, we get a remainder of 5 on the lhs(all odd squares have remainder 1 when divided by 8) while on the rhs we have remainder 1 (since u and v are both odd if m, n both odd)Show that 4m^2+17n^2 and 4n^2+17m^2 cannot be both be perfect squares, where n, and m are positive integers
SetFind all functionssuch that
for all rational.
(Note thatis the set of rational numbers.)
I tried that as well as plugging in
Yep I got that for