Solve the equation: `|[x,2,3],[4,x,1],[x,2,5]|=0 `

Solve the equation: |[2,3],[4,5]|=|[x,3],[2x,5]|

Solve the equation: |[3,x],[x,1]|=|[3,2],[4,1]|

Solve the equation: x^(2)+3x+5=0

Solve the equation 2|x-2|-3|x+4|=1

Solve the equation 2x+3[x]-4{-x}=4

Solve the equation x^(2)-4x+[x]+3=0

Solve the equation 5^(x^(2)+3x+2)=1

Solve the equation 2x^(2)+ 5x-12=0

Solve the equation 2x^(2)+5x-12=0

(i) Solve the equation |{:(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,2x-64):}|=0 (ii) Prove that x = 1 is a root of the equation (ii) Prove that x=1 is a root of the following equation |{:(x+1,3,5),(2,x+2,5),(2,3,x+4):}|=0 Also find the remaining roots. (iii) If a+b+c=0 then solve |{:(a-x,c,b),(c,b-x,a),(v,a,c-x):}|=0 (iv) Solve |{:(6-x,3,3),(3,4-x,5),(3,5,4-5):}|=0