Write the result after applyin componendo and dividendo to `3a^(2)+2b^(2):3a^(2)-2b^(2): :3c^(2)+2d^(2):3c^(2)-2d^(2)`.

If D is the mid-point of the side BC of triangle ABC and AD is perpendicular to AC, then 3b^(2)=a^(2)-c( b )3a^(2)=b^(2)3c^(2)b^(2)=a^(2)-c^(2)(d)a^(2)+b^(2)=5c^(2)

If a, b, c and d are in proportion, then show that (a^(3)+3ab^(2))/(3a^(2)b+b^(3))=(c^(3)+3cd^(2))/(3c^(2)d+d^(3))

If a/b = c/d = e/f , then prove that each of these ratio's is equal to ((4a^(2)+3c^(2)-7e^(2))/(4b^(2)+3d^(2)-7f^(2)))^(1//2)

If a!=0 and the line 2bx+3cy+4d=0 passes through the points of intersection of the parabolas y^(2)=4ax and x^(2)=4ay, then: d^(2)+(2b+3c)^(2)=0 (b) d^(2)+(3b+2c)^(2)=0d^(2)+(2b-3c)^(2)=0 (d) d^(2)+(3b-2c)^(2)=0

If a!=0 and the line 2bx+3cy+4d=0 passes through the points of intersection of the parabolas y^(2)=4ax and x^(2)=4ay, then of (a)d^(2)+(2b+3c)^(2)=0(b)d^(2)+(3b+2c)^(2)=0(c)d^(2)+(2b-3c)^(2)=0 (d)none of these

if a , b , c and d are in proportion, prove that : (i) (a-b)/(c-d)= sqrt((3a^(2) + 8b^(2))/(3c^(2) + 8d^(2))) (ii) ((5a^(2) + 12c^(2))/(5b^(2) + 12d^(2))) = sqrt((3a^(4) - 7c^(4))/(3b^(4) - 7d^(4)))

(d^(2))/(dx^(2))(x^(2)+3x+2)= (A) 2x+3 (B) 2 (C) 3 (D) 2x

In a parallelogram ABCD, |bar(AB)|=a,|bar(AD)|=b and |bar(AC)|=c, then bar(DB).bar(AB) has the value: (A) (3a^(2)+b^(2)-c^(2))/(2) (B) (a^(2)+3b^(2)-c^(2))/(2) (c) (a^(2)-b^(2)+3c^(2))/(2) (D) (a^(2)+3b^(2)+c^(2))/(2)

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then 3b^2=a^2-c ^2 (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2