If 3x + 2y = 12 and xy = 6 find the value of 9x squared + 4y squared
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XY=6
x=6/y
putting in
3x+2y=12
3(6/y)+2y=12
18/y+2y=12
18+2y²/y=12
2(9+y²)=12
9+y²=6
y²=-3
y=√-3
putting in
XY=6
x=6/√-3
x=-2√3
then
9x²+4y²
9(-2√3)²+4(√-3)²
108+12
120
x=6/y
putting in
3x+2y=12
3(6/y)+2y=12
18/y+2y=12
18+2y²/y=12
2(9+y²)=12
9+y²=6
y²=-3
y=√-3
putting in
XY=6
x=6/√-3
x=-2√3
then
9x²+4y²
9(-2√3)²+4(√-3)²
108+12
120
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