`(2x - 1/2)(3x/2 - 1/4)`

Let the equation x^(5) + x^(3) + x^(2) + 2 = 0 has roots x_(1), x_(2), x_(3), x_(4) and x_(5), then find the value of (x_(1)^(2)-1)(x_(2)^(2) - 1)(x_(3)^(2) - 1)(x_(4)^(2) - 1)(x_(5)^(2) - 1).

Simplify: (i) {(1/3)^(-3)-\ (1/2)^(-3)}-:(1/4)^(-3) (ii) (3^2-\ 2^2)x\ (2/3)^(-3) (iii) {(1/2)^(-1)x\ (-4)^(-1)}^(-1) (iv) [{((-1)/4)^2}^(-2)]^(-1) (v) {(2/3)^2}^3x\ (1/3)^(-4)x\ 3^(-1)x\ 6^(-1)

If I=intdx/(x^4sqrt(a^2+x^2)),t h e nI equals 1/(a^4)[1/xsqrt(a^2+x^2)-1/(3x^3)sqrt(a^2+x^2)]+c 1/(a^4)[1/xsqrt(a^2+x^2)-1/(3x^3)(a^2+x^2)^(3//2)]+c 1/(a^4)[1/xsqrt(a^2+x^2)-1/(2sqrt(x))(a^2+x^2)^(3//2)]+c 1/(a^4)[1/xsqrt(a^2+x^2)+1/(3x^3)sqrt(a^2+x^2)]+c

The value of lim_(xto oo)(2x^(1//2)+3x^(1//3)+4x^(1//4)+....nx^(1//n))/((2x-3)^(1//2)+(2x-3)^(1//3)+....+(2x-3)^(1//n)) is

The value of lim_(xto oo)(2x^(1//2)+3x^(1//3)+4x^(1//4)+....nx^(1//n))/((2x-3)^(1//2)+(2x-3)^(1//3)+....+(2x-3)^(1//n)) is

Solve for : x :(x-1)/(x-2)+(x-3)/(x-4)=3 1/3,x!=2,4

Solve for x : (x-1)/(x-2)+(x-3)/(x-4)=3 1/3;\ \ x!=2,\ 4

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

lim_(x->a){[(a^(1/2)+x^(1/2))/(a^(1/4)-x^(1/4)))^(- 1)-(2(a x)^(1/4))/(x^(3/4)-a^(1/4)x^(1/2)+a^(1/2)x^(1/4)-a^(3/4))]^(- 1)-sqrt2^(log_4 a)}^8

(lim)_(xvecoo)(2. x^(1//2)+3. x^(1//3)+4. x^(1//4)++ndotx^(1//n))/((3x-4)^(1//2)+(3x-4)^(1-3)+(3x-4^)^(1//3)++(3x-4)^(1//n)) (here n in N ,ngeq2 ) is equal to 1 dot2/(sqrt(3)) 2. (sqrt(3))/2 3. 1/2 4. 1/(sqrt(3)) 5. 2