If `3x - (1)/(3x ) =5`, find : (i) `9x^(2) + (1)/( 9x^2)`

If 3x + (1)/(3x) = 3 , find : (i) 9x^(2) + (1)/(9x^2)

If x gt 0 and x^(2) +(1)/(9x^(2))= (25)/(36) , find x^(3) + (1)/(27x^(3))

If 7x - 15y = 4x + y , find the value of x: y . Hence, use componendo and dividendo to find the values of : (i) (9x + 5y)/(9x - 5y) (iI) (3x^(2) + 2y^(2))/(3x^(2) - 2y^(2))

If x= -5 + sqrt(-16) , find the value of x^(4) + 9x^(3) + 35x^(2)-x + 4

Using properties of proportion, solve for x : (i) (sqrt(x + 5) + sqrt(x - 16))/ (sqrt(x + 5) - sqrt(x - 16)) = (7)/(3) (ii) (sqrt(x + 1) + sqrt(x - 1))/ (sqrt(x + 1) - sqrt(x - 1)) = (4x -1)/(2) . (iii) (3x + sqrt(9x^(2) -5))/(3x - sqrt(9x^(2) -5)) = 5 .

If f(x)=3x^4-5x^2+9, find f(x-1) .

int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k _(1)) ( sqrt(1-9x ^(2))+ (cos ^(-1) 3x )^(k_(2)))+c, then k _(1) ^(2)+k_(2)^(2)= (where C is an arbitrary constnat. )

If |3x | != 2 , what is the value of (9x^2 - 4)/(3x + 2) - (9x^2 - 4)/(3x - 2) ?

Find the sum of the following algebraic expressions : 3x^(3) - 5x^(2) + 2x + 1 , 3x - 2x^(3) - x^(3) , 2x^(2) - 7x + 9

Simplify the following : 5x^(4) - 7x^(2) +8x - 1 +3x^(2) - 9x^(2) + 7 - 3x^(4)+11x - 2 +8x^(2)