If the slope of one of the lines represented by ax2+2hxy+by2=0 is the square of the other, then a+bh+8h2ab=

Let m and m2 be the slopes of the lines represented by ax2+2hxy+by2=0. Then,     m+m2=−2hb and     mm2=ab or m3=ab∴    m+m23=−2hb3∴    m3+m6+3mm2m+m2=−8h3b3ab+ab2+3ab-2hb=−8h3b3∴    ab2(a+b)+8h3b3=6ahb2Multiply both sides by b2ah∴ a+bh+8h2ab=6