" (i) "(a-c)^(2)=4(a-b)(b-c)

If a,b,c are in A.P. prove that (a-c)^(2)=4(a-b)(b-c)

If a,b,c are in A.P.show that (a-c)^(2)=4(a-b)(b-c)

If a,b,c are in A.P.,prove that: (a-c)^(2)=4(a-b)(b-c)a^(2)+c^(2)+4ac=2(ab+bc+ca)a^(3)+c^(3)+6abc=8b^(3)

|[a^(2), b^(2), c^(2)], [(a+1)^(2), (b+1)^(2), (c+1)^(2)], [(a-1)^(2), (b-1)^(2), (c-1)^(2)]| =-4(a-b)(b-c)(c-a)

6.The roots of the equation (a-b+c)x^(2)+4(a-b)x+(a-b-c)=0 are

The value of [{(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3}/{(a-b)^3+(b-c)^3+(c-a)^3}] = (1) 3(a+b)(b+c)(c+a) (2) 3(a-b)(b-c)(c-a) (3) (a+b)(b+c)(c+a) (4) 1

Proove that 2b^2c^2+2c^2a^2+2a^2b^2-a^4-b^4-c^4=(a+b+c)(b+a-c)(c+a-b)(a+b-c)

Prove that |(1+a^(2)+a^(4),1+ab+a^(2)b^(2),1+ac+a^(2)c^(2)),(1+ab+a^(2)b^(2),1+b^(2)+b^(4),1+bc+b^(2)c^(2)),(1+ac+a^(2)c^(2),1+bc+b^(2)c^(2),1+c^(2)+c^(4))|=(a-b)^(2)(b-c)^(2)(c-a)^(2)

Using factor theorem, show that |(-2a,a+b,c+a),(a+b,-2a,b+c),(c+a,c+b,-2c)|=4(a+b)(b+c)(c+a)

Consider a circle x^2+y^2+a x+b y+c=0 lying completely in the first quadrant. If m_1a n dm_2 are the maximum and minimum values of y/x for all ordered pairs (x ,y) on the circumference of the circle, then the value of (m_1+m_2) is (a) (a^2-4c)/(b^2-4c) (b) (2a b)/(b^2-4c) (c) (2a b)/(4c-b^2) (d) (2a b)/(b^2-4a c)