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Question

The linear factor(s) of the equation 9x2−24xy+16y2−12x+16y−12=0 is/are

A
3x2y+2=0
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B
3x2y+6=0
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C
3x4y6=0
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D
3x4y+2=0
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Solution

The correct option is D 3x4y+2=0
9x224xy+16y212x+16y12=0
Writing equation in terms of y, we get
16y2+(24x+16)y+(9x212x12)=0
Now, using quadratic formula, we have
y=24x16±(24x+16)2416(9x212x12)216y=24x16±64(3x2)264(9x212x12)216y=24x16±8(9x2+412x)(9x212x12)216y=3x2±44y=3x+24 or y=3x64
​​​​​​​3x4y+2=0 or 3x4y6=0



Alternate Solution:
9x224xy+16y212x+16y12=0(9x224xy+16y2)4(3x4y)12=0(3x4y)24(3x4y)12=0
(3x4y+2)(3x4y6)=0
​​​​​​​​​​​​​​3x4y+2=0 or 3x4y6=0



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