`a`, `b` be roots of x^2-1154x+1=0, then find the value of (a)^1/4+(b)^1/4.

According to the equation given, a+b=1154 and ab=1. let a^1/4+b^1/4= k k^2= a^1/2+b^1/2+2(ab)^1/4 Since ab=1 k^2= a^1/2+b^1/2+2 root A+ root b= k^2-2........(This value is important) k^4= a+b+4+2(ab)^1/2+4 root A+ 4 root B k^4= 1154+2+4+4(k^2-2) Final equation is easy to solve and simplified k^4-4 k^2-1152; put k^2=x and solve the equation to get x=36 or k^2=36 so k is our answer which is equal to 6. I recommend to copy down the whole solution to understand properly

According to the equation given, a+b=1154 and ab=1. let a^1/4+b^1/4= k k^2= a^1/2+b^1/2+2(ab)^1/4 Since ab=1 k^2= a^1/2+b^1/2+2 root A+ root b= k^2-2........(This value is important) Now calculate k^4 and we get k^4=a+b+4+2(ab)^1/2+4(root A + root B ) replace the root A+ root B value to form a biquadratic equation of k k^4-4k^2-1152---> This equation is very easy to solve let k^2=x and solve for x to get x=36 or k^2= 36 or k=6 Hence we get k=6 that is our answer I guess