Without expanding, show that the value of each of the determinants is zero: `|[(2^x+2^(-x))^2, (2^x-2^(-1))^2, 1] , [(3^x+3^(-1))^2, (3^x-3^(-x))^2, 1] , [(4^x+4^(-x))^2, (4^x-4^(-x))^2, 1]|`

If x,y,zepsilonR then the value of |((2x^(x)+2^(-x))^(2),(2^(x)-2^(-x))^(2),1),((3x^(x)+3^(-x))^(2),(3^(x)-3^(-x))^(2),1),((4^(x)+4^(-x))^(2),(4^(x)-4^(-x))^(2),1)| is

Without expanding, show that the value of each of the following determinants is zero: |1^2 2^2 3^2 4^2\ \ \ 2^2 3^2 4^2 5^2\ \ \ 3^2 4^2 5^2 6^2\ \ \ 4^2 5^2 6^2 7^2| (ii) |a b c a+2x b+2y c+2z x y z| (iii) |(2^x+2^(-x))^2(2^x-2^(-x))^2 1(3^x+3^(-x))^2(3^x-3^(-x))^2 1(4^x+4^(-x))^2(4^x-4^(-x))^2 1|

Solve each of the following equatins : ((2x-3)/(x-1))-4((x-1)/(2x-3))=3,xne1,(3)/(2)

Find the value of x in each of the following cases : (i) 3^(2x+3)=1" "(ii)2^(x-5)xx5^(x-4)=5 (iii)2^(2x+1)=2^(2x-1)+12" "(vi)3^(2x-3)=3sqrt(3)

By using properties of determinants. Show that: |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=(1-x^3)^2

The complete set of values of x satisfying the equation x^2. 2^(x+1)+2^(|x-3|+2)=x^2. 2^(|x-3|+4)+2^(x-1) is

Which of the following is a zero of the polynomial x^(3)-x^(3)+2x-2 1. 1 2. -1 3. 2 4. -2

Solve the equations: 4^(x)-3^(x-(1)/(2))=3^(x+(1)/(2))-2^(2x-1) .

Determine the values of x for which the matrix A= [(x+1,-3 ,4),(-5,x+2, 2) ,(4 ,1,x-6)] is singular.

The greatest value of the function f(x)=2. 3^(3x)-3^(2x). 4+2. 3^x in the interval [-1,1] is