AP EAMCET2013MathematicsTrigonometric Equations
The set of solutions of the system of equations aligned x+y & = 2 3 and x+ y & = 3 2 , aligned where x, y are real, is
Options
- A(x, y): ( x-y 2 )= 1 2
- B(x, y): ( x-y 2 )= 1 2
- C(x, y): (x-y)= 1 2
- DEmpty set
Correct answer
D. Empty set
Step-by-step solution
Given system of equation is x+y= 2 3 and x+ y= 3 2 , where x, y are real. aligned & 2 ( x+y 2 ) ( x-y 2 )= 3 2 & ( 1 2 2 3 ) ( x-y 2 )= 3 4 aligned [from Eq. (i)] aligned & ( 3 ) ( x-y 2 ) & = 3 4 & 1 2 ( x-y 2 ) & = 3 4 & ( x-y 2 ) & = 3 2 aligned Now, we have aligned & (x-y)=2 ^2 ( x-y 2 )-1 & .=2 9 4 -1= 9 2 -1= 7 2 [from Eq. (ii) ] & and (x-y)=1-2 ^2 ( x-y 2 ) & ( x-y 2 ) < 0 & aligned So, system of equation have empty set of solution.