y2+3xy-12x2
= (y2+3xy+\(\dfrac{9}{4}x^2\) )-\(\dfrac{57}{4}x^2\)
= \(\left(y+\dfrac{3}{2}x\right)^2-\dfrac{57}{4}x^2\)
=\(\left(y+\dfrac{3}{2}-\dfrac{\sqrt{57}}{2}\right)\left(y+\dfrac{3}{2}+\dfrac{\sqrt{57}}{2}\right)\)
y2+3xy-12x2
= (y2+3xy+94x294x2 )-574x2574x2
= (y+32x)2−574x2(y+32x)2−574x2
=(y+32−√572)(y+32+√572)