Poland Junior Math Olympiad - Algebra Problem

Poland Junior Math Olympiad - Algebra Problem

[johngreen]

Again I did this problem a little bit differently a = 7 +4*3^(1/2) then a - 7 = 4*3^(1/2) sguaring both sides gives a^2 -14a + 49 = 48 so a^2+1 =14a or (a^2+1)/a =14 which gives you a +1/a= 14
now squaring again gives you a^2- 1/a^2+ 2= 14^2 = 196 simplfying gives you a^2+1/a^2= 194

[prabhudasmandal]

I did it this way. Given expression is a^2+b^2) /(ab) ^2.(simplified). Now the given value a=7+4√3 and ab=1.ab=1 orb=1/aor 1/7+4√3or rationalising it is 7--4√3.so, (a^2+b^2) ={7+4√3) ^2+(7--4√3) ^2=194and a^2b^2 is 1.so, the result is 194.

[gyandensity]

Aisa question bahut sara lao maja aata hai banane mei