Problem type 7 :-
now , we come such problems where we only think and waste our time and don't get any conclusion and 2-3 mins are spoiled
if x+y+z=0 , then x^2/yz+y^2/zx+ z^2/xy =?
now , we see if x+y+z = 0 , then x=1 , y=2 , and z= -3 ... will satisfy it ...
so , (1/-6) + (4/-3) + 9/2 = 3 ... there are options in such a way :-
(xyz)^2 ......... 3 ............ 9 ............. x^2+y^2+z^2 ... so , no confusion only 3 .... if any confusion arises , change the values :)
one more type is where we have to do rationalization ....
let's begin :-
if x= rt(3) +rt(2) , then what is the value of x^2+1/x^2 ...=? ..
now , we quickly do square and add and blah blah ........ stop dude ...
see x=rt(3) + rt(2) ... 1/x = 1/rt(3)+rt(2) now , rationalize it , we get ... 1/x= rt(3)-rt(2)
now , x^2+1/x^2 = (3+2)*2 = 10 ..
problem type 8:-
if a>b , and a+b =5 , ab=6 ... then , a^2-b^2 = ? ..
now , we go to the solution side .....
we quickly find a-b by (a-b)^2 = (a+b)^2 - 4ab and then solve it .... that must be the strategy but look here , when very small values come , then try your logic rather than calculating which always make error called silly mistakes in exams ... always avoid long calculation ..
now , a+b=5 , ab=6 .. then 3,2 are only such factors and when a>b , then , a=3 , b=2 ... a^2-b^2=4 ... sometimes , use clever way rather than rota way ;)