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Question

If the equation x2+9y24x+3=0 is satisfied for all real values of x and y, then

A
x[1,3]
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B
y[13,13]
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C
x(13,3]
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D
y(3,13)
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Solution

The correct options are
A x[1,3]
B y[13,13]
Given equation is
x2+9y24x+3=0 ...(1)
The above equation is quadratic in terms of both variables x and y.

Case 1: Considering equation (1) as quadratic equation in terms of x
x24x+(9y2+3)=0
For xRD0
164(9y2+3)09y21y[13,13]

Case 2: Considering equation (1) as quadratic equation in terms of y
9y2+0y+(x24x+3)=0
For yRD0
04×9×(x24x+3)0x24x+30x[1,3]

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