They might be simple, But mujhse accurately kabhi nahi hote...in search fr a strategic approach.
Find the number of ordered pairs (x,y) (Both x, y are integers) Satisfying-
Q1) 2x2 -3xy -2y2 =7
Q2) y- lx2-2xl +1/2 >0 & y+ l x-1l < 2
11The 1st qsn simply requires a factorisation and the fact that 7 is prime....
13Hey, i did smthing...! But it needs 2b verified 1st..
Q1) Writing as-
2(x+y)(x-y) -3xy =7
So, v need to find, α & β such tht...
2α - 3β =7
Taking- α=8, β=3 satisfies.
So, xy=3 & , x2-y2 =8
Solving fr x, we get ......x=±3 => y= ±1
Hence integral solutions = 2
Okay, so this finally giving the answer, but how do v convince ourselves tht there are no other values of α,β satisfying the above condition & giving integral solutions fr x & y....?
Also, the 2nd one's left still...
11Why don't u simply write the 1st expression as (2x+y)(x-2y)=7....? Where do u get alpha-beta and all those stuff?
13Arrey, am telling u, this factorisation thing never clicks me at all...!! Have tried a lot !
Theek hai... (2x+y)(x-2y)=7, phir next ?
11AAre....now since 7 is prime, so only factors are 7 and 1, so either 2x+y=7 (or 1), similarly x-2y=1 (or 7), now simultaneously solve both. Any more doubts?
112nd wala -- - - - - -
I'm feeling lazy to go for it, u just need to take a few intervals for this....
132nd waala ho jayegaa ab, i think, wahi mod ki Qty ko +ve/-ve lena hai na; with appropriate intervals ? Then, graph...