`|((x-2)^2,(x-1)^2,x^2),((x-1)^2,x^2,(x+1)^2),(x^2,(x+1)^2,(x+2)^2)|=-8.`

IF ax^3+bx^2+cx+d = |(x^2,(x-1)^2, (x-2)^2),((x-1)^2 (x-2)^2, (x-3)^2), (x-2)^2, (x-3)^2, (x-4)^2)| , then d= (A) 1 (B) -8 (C) 0 (D) none of these

IF ax^3+bx^2+cx+d = |(x^2,(x-1)^2, (x-2)^2) ,((x-1)^2, (x-2)^2, (x-3)^2), ((x-2)^2, (x-3)^2, (x-4)^2)| , then d= (A) 1 (B) -8 (C) 0 (D) none of these

x^(2)+(1)/(x^(2))-7(x-(1)/(x))+8

Prove that |(1,x,x^2),(x^2,1,x),(x,x^2,1)|=(1-x^2) .

(iv) ((2x+1)/(x+1))^(4)-6((2x+1)/(x+1))^(2)+8=0

(x^(2))/(x+1)+((x+1)^(2))/(x^(2))-(x)/(x+2)+(x+1)/(x)-(7)/(4)=p^(2)

int((x^(- 6)-64)/(4+2x^(- 1)+x^(- 2))*(x^2)/(4-4x^(- 1)+x^(- 2))-(4x^2(2x+1))/(1-2x))dx

Check whether the following are quadratic equations : (1) (x-1)^(2)=2(x-3) (2) x^(2)-2x=(-2)(3-x) (3) (x-2)(x+1)=(x-1)(x+3) (4) (x-3)(2x+1)=x(x+5) (5) (2x-1)(x-3)=(x+5)(x-1) (6) x^(2)+3x+1=(x-2)^(2) (7) (x+2)^(3)=2x(x^(2)-1) (8) x^(3)-4x^(2)-x+1=(x-2)^(3)

(x^(2))/((x+1)^(2))+((x+1)^(2))/(x^(2))-(x)/(x+1)+(x+1)/(x)-(7)/(4)=p^(2)