已知9x^2-12xy+4y^2+30x-20y+25=0,求9x^2-12xy+4y^2的值

已知9x^2-12xy+4y^2+30x-20y+25=0,求9x^2-12xy+4y^2的值
已知9x^2-12xy+4y^2+30x-20y+25=0,求9x^2-12xy+4y^2的值

已知9x^2-12xy+4y^2+30x-20y+25=0,求9x^2-12xy+4y^2的值
已知9x^2-12xy+4y^2+30x-20y+25=0,
(3x-2y)^2+10(3x-2y)+5^2=0
(3x-2y+5)^2=0
3x-2y=-5
(3x-2y)^2=25
9x^2-12xy+4y^2=(3x-2y)^2=25

9x^2-12xy+4y^2+30x-20y+25=0
(3x-2y)²-10(3x-2y)+5²=0
(3x-2y-5)²=0
即
3x-2y-5=0
3x-2y=5
所以
9x^2-12xy+4y^2
=（3x-2y）²
=5²
=25