|[1,7,x^(2)],[x^(2),1,x],[x,x^(2),1]|

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,x,x^2),(x^2,1,x),(x,x^2,1):}|=(1-x^3)^2

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

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

Value of |{:(1+x_(1),,1+x_(1)x,,1+x_(1)x^(2)),(1+x_(2),,1+x_(2)x,,1+x_(2)x^(2)),(1+x_(3),,1+x_(3)x,,1+x_(3)x^(2)):}| depends upon

If x,y,z in R , then the value of determinant |((5^(x)+5^(-x))^(2) , (5^(x)-5^(-x))^(2),1),((6^(x)+6^(-x))^(2),(6^(x)-6^(-x))^(2), 1),((7^(x)+7^(-x))^(2),(7^(x)-7^(-x))^(2),1)| is

If |{:(x^(2) +x , 3x - 1 , -x + 3),(2x +1 , 2 + x^(2) , x^(3) - 3),(x - 3, x^(2) + 4, 3x):}| = a_(0) + a_(1) x + a_(2) x^(2) + .... + x_(7) x^(7), then the value of a_(0) is

If x_(1),x_(2),x_(3)=2xx5xx7^(2), then the number of solution set for (x_(1),x_(2),x_(3)) where x_(1)in N,x_(i)>1 is

(x^(2)-x-1)(x^(2)-x-7)<-5

If y=(x^(7/2)+x^(-1/2))/(x^(7/2)-x^(-1/2)) , then (dy)/(dx)=

The constant term in the expansion of [(3x+1,2x-1,x+2),(5x-1,3x+2,x+1),(7x-2,3x+1,4x-1)] is