Recent content by Hazel

Got it! Thanks. :D

Oh thank you so much Mark! I have been on this problem for HOURS! The example never told me I needed a common denominator. You couldn't have explained it better! Thanks so much!

Ok I see you added n+5 to both sides. I'm going to try this on my exercise to see if I can get it now. Thanks! - - - Updated - - - I still do not see have they got 1/2k(k+9)+[k+1)+4] simplified to: 1/2(K^2+11k+10)

Original Equation: 5+6+7+...+(n+4)=1/2n(n+9) Ok, I've tried everything to understand this. I'm just not getting it. I understand everything (n=1, k+1, etc) up until this point: "To continue with proof what must be done?". I know you must simplify the right side, but I don't understand how they...

Thanks! Solved!

Actually it's: (12,1) (-12,-1) (\sqrt{78},\sqrt{78}) (-\sqrt{78},-\sqrt{78}) My mistake

Right? (1,12) (-1,-12) (\sqrt{78},\sqrt{78}) (-\sqrt{78},-\sqrt{78})

(12y)^2+(12y)y=156 144y^2+12y^2=156 156y^2=156 y^2=1 y=\pm\sqrt{1} y=\pm1 x^2+x(x)=156 x^2+x^2=156 2x^2=156 x^2=78 x=\pm\sqrt{78}

Using x^2+xy=156? x=12y x=y So 1st it will be: (12y)^2+(12y)y=156? Then: (y)^2+(y)y=156?

x^2-13xy+12y^2=0 (x-12y)(x-y)=0 x=12y x=y

x^2-13xy+12y^2=0 (1) x^2+xy=156 (2) What I have so far: x^2+xy=156 xy=156-x^2 y=(156-x^2)/x) Plugged y=(156-x^2)/x) into (1): x^2-13x(156-x^2)/x)+12(156-x^2)/x)^2=0 For 1st half I Multiplied x to -13x in order to get the same denominator so I can multiply it to (156-x^2)/x)...