If `x > 2 and x < 3`, then which of the following is positive?
I. `(x - 2)(x - 3)`
II. `(2 - x)(x - 3)`
III. `(2 - x)(3 - x)`

Factorise (i) x ^(2) - 2x ^(2) - x +2 (ii) x ^(3) - 3x ^(2) - 9x -5 (iii) x ^(3) + 13 x ^(2) + 32 x + 20 (iv) y ^(3) + y ^(2) -y -1

(i) (x ^ (3) + 2x ^ (2) + 3x) -: 2x (ii) (10x-25) - :( 2x-5) (iii) (x (x + 1) (x + 2 ) (x + 3)) - :( x (x + 1))

Use suitable identities to find the following products (i) (x +5) (x +2) (ii) (x-5) (x-5) (iii) (3x +3) (3x -2) (iv) (x ^(2) + (1)/( x ^(2)) )(x ^(2) - (1)/( x ^(2))) (v) (1+x) (1+x)

Use suitable idntities to find the following products (i) (x +5) (x +2) (ii) (x-5) (x-5) (iii) (3x +3) (3x -2) (iv) (x ^(2) + (1)/( x ^(2)) )(x ^(2) - (1)/( x ^(2))) (v) (1+x) (1+x)

Use suitable idntities to find the following products (i) (x +5) (x +2) (ii) (x-5) (x-5) (iii) (3x +3) (3x -2) (iv) (x ^(2) + (1)/( x ^(2)) )(x ^(2) - (1)/( x ^(2))) (v) (1+x) (1+x)

Find x, if : (i) log_(2) x = -2 (ii) log_(4) (x + 3) = 2 (iii) log_(x) 64 = (3)/(2)

If x=3+2sqrt(2) , find : (i) (1)/(x) (ii) x-(1)/(x) (iii) (x-(1)/(x))^(3) (iv)x^(3)-(1)/(x^(3))