Fill ups
If `x+1/x=sqrt6`, then the value of `x^2+1/x^2`=………..

If x=1/(2-sqrt3) find the value of x^3-2x^2-7x+5 .

If x=(sqrt3+1)/2 find the value of 4x^3+2x^2-8x+7

Let S(x)=1+x-x^(2)-x^(3)+x^(4)+x^(5)-x^(6)-x^(7)+"........+"oo , where 0ltxlt1 . If S(x)=(sqrt(2)+1)/(2) , then the value of (x+1)^(2) is

If f(x) = {{:(((pi)/(2)-sin^(-1)(1-{x}^(2))sin^(-1)(1-{x}))/(sqrt(2) ({x} - {x}^(3)))",",x gt 0),(k",",x = 0),((A sin^(-1)(1-{x})cos^(-1)(1-{x}))/(sqrt(2{x})(1-{x}))",",x lt 0):} is continuous at x = 0, then the value of sin^(2) k + cos^(2) ((Api)/(sqrt(2))) , is..... (where {.} denotes fractional part of x).

Fill in the blanks: If cos(tan^-1 x + cot^-1 sqrt3) = 0 , then value of x is ………

Given 0 le x le 1/2 , then the value of : tan[sin^-1(x/sqrt2 + (sqrt(1-x^2))/sqrt2)- sin^-1x] is

If |A| = 2 and A = | (2x, 6) , (5x, 1)| then find the value of x

If cos^(-1).(6x)/(1 + 9x^(2)) = -(pi)/(2) + 2 tan^(-1) 3x , then find the values of x

If {:|(x,2),(8,x)| = |(3,2),(9,6)| , then the value of 'x' is …………. (fill in the blanks).