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Find the integral values of K for which the system of equations possess solution and find those solutions

Find the integral values of K for which the system of equations possess solution and find those solutions

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Grade:11

1 Answers

Aditya Gupta
2081 Points
5 years ago
hello govind i am getting my answer as k=2, y= ±1 and x= cos((pi/2)^2).
simply keep arccosx= A and (arcsiny)^2= B. then A+B and AB are given.
so z^2 – (A+B)z + AB= 0 will have roots A and B.
or z^2 – (kpi^2/4)z + pi^4/16= 0 will have roots A and B.
but A and B need to be real. so the discrimiinant shouldbe greater than zero, which would imply k is greater than equal to 2, as k is positive. also since k is an integer, the next possible values of k can be 3, 4, 5,.... but max value of A+B is always less than 3pi^2/4, so that k can never be greater than or equal to 3. hence k=2.
once you put k=2,  z^2 – (kpi^2/4)z + pi^4/16= (z – (pi/2)^2)^2=0
or A=B=(pi/2)^2, whence you can see that y= ±1 and x= cos((pi/2)^2).

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