Solve the equation `(x-a)^(1/2)(x-b)^(1/2)-(x-c)^(1/2)(x-d)^(1/2)=(a-c)^(1/2)(b-d)^(1/2)`

If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))| = (a - b) (b - c) (c - a) (a + b + c) , where a,b,c are all different, then the determinant |(1,1,1),((x-a)^(2),(x-b)^(2),(x-c)^(2)),((x-b)(x-c),(x-c)(x-a),(x-a)(x-b))| vanishes when a)a + b + c = 0 b) x = (1)/(3) (a + b + c) c) x = (1)/(2) (a + b + c) d) x = a + b + c

The sum of the solution of the equation 2sin^(-1)sqrt(x^(2)+x+1)+cos^(-1)sqrt(x^(2)+x)=(3 pi)/(2) is 0(b)-1( c) 1 (d) 2

(x)/(x-1)+(1)/(x+1)+(2x)/(1-x^(2))=?( a) 1 (b) 2 (c) 3(d)4

Solve the equations. sin(tan^(-1)x),|x|<1 (a) x/(sqrt(1-x^2)) (B) 1/(sqrt(1-x^2)) (C) 1/(sqrt(1+x^2)) (D) x/(sqrt(1+x^2))

Solve the equations. sin(tan^(-1)x),|x|<1 (A) x/(sqrt(1-x^2)) (B) 1/(sqrt(1-x^2)) (C) 1/(sqrt(1+x^2)) (D) x/(sqrt(1+x^2))

int(x+1)/(x^(1//2)) dx= a) -x^(3//2)+x^(1//2)+c b) x^(1//2 c) 2/3x^(3//2)+2x^(1//2)+c d) x^(3//2)+x^(1//2)+c

The sum of roots of equation (1)/(x+a)+(1)/(x+b)=(1)/(c) is zero find the product of roots of equation a)0b ) ((a+b)/(2))c)-((a^(2)+b^(2))/(2))d(a^(2)+b^(2))

The number of roots of the equation,x-(2)/(x-1)=1-(2)/(x-1) is 0(b)1(c)2(d)3

The sum of the solution of the equation 2sin^(-1)sqrt(x^2+x+1)+cos^(-1)sqrt(x^2+x)=(3pi)/2 is 0 (b) -1 (c) 1 (d) 2

The sum of the solution of the equation 2sin^(-1)sqrt(x^2+x+1)+cos^(-1)sqrt(x^2+x)=(3pi)/2 is 0 (b) -1 (c) 1 (d) 2