If x,y∈R and 2x2+6xy+5y2=1, then

2x2+6xy+5y2=1                 (1)Equation (1) can be rewritten as2x2+(6y)x+5y2−1=0Since x is real, we have36y2−85y2−1≥0or   y2≤2or   −2≤y≤2Equation (1) can also be rewritten as          5y2+(6x)y+2x2−1=0Since y is real, we have           36x2−202x2−1≥0or   36x2−40x2+20≥0or   −4x2≥−20or   x2≤5or  −5≤x≤5