If `[[x^2-4x,x^2],[x^2,x^3]]`=`[[-3,1],[-x+2,1]]` (then find x)

If |[1, x, x^2], [x, x^2, 1], [x^2, 1, x]|=3, then find the value of |[x^3-1, 0, x-x^4], [0, x-x^4, x^3-1], [x-x^4, x^3-1, 0]|

If f(x) = |[x^2-4x+6,2x^2+4x+10,3x^2-2x+16],[x-2,2x+2,3x-1],[1,2,3]| then find the value of int_(-3)^3(x^2sinx)/(1+x^6)f(x) dx .

The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,4x^2,1+8x^3] , [3x, 9x^2,1+27x^3]|=10 is (A) 0 (B) 1 (C) 2 (D) 3

" If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3x-1,,3x,,3x-3),(x^(2)+2x+3,,2x-1,,2x-1):}|=xA +B then find A and B

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

If x^4+1/(x^4)=194 ,\ find x^3+1/(x^3),\ x^2+1/(x^2) and x+1/x

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+1/x=3, calculate x^2+1/(x^2),\ x^3+1/(x^3) and x^4+1/(x^4)

If x^4+1/(x^4)=194 , find x^3+1/(x^3),x^2+1/(x^2) and x+1/x