4Thanks Nishant Sir
& Arshad
If the eqn 2x2 +4xy + 7y2 - 12x - 2y + t = 0 where 't' is a parameter has exactly one real solution of the form (x,y) . Then the sum of (x+y) is equal to
(A) 3
(B) 5
(C) - 5
(D) -3
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5 Answers
1just partially differentiate with respect to x
and den with respect to y
u will get two equation solve dem simultaneously to get the value of x and y
62Or alternatively
\\2x^2+4xy+7y^2-12x-2y+t=0 \\2x^2+4x(y-3)+7y^2-2y+t=0 \\\text{this is a quadratic in x with only one real soln. Hence D=0} \\(4(y-3))^2=4.2.(7y^2-2y+t) \\2(y^2-6y+9)=7y^2-2y+t \\2y^2-12y+18=7y^2-2y+t \\5y^2+10y+t-18=0 \\\text{for on root, D=0 again} \\10^2=4.5.(t-18) \\t=23
if t=23, then y=-1
and if y = -1, the original quadratic gets reduced to
\\2x^2-16x+32=0
hence x=4
so x+y=3