Home
Class 12
MATHS
The minimum value of ((x+1/x)^6-(x^6+1/...

The minimum value of `((x+1/x)^6-(x^6+1/(x^6))- 2)/((x+1/x)^3+x^3+1/x^3)` is (for x>o)

Text Solution

Verified by Experts

The correct Answer is:
6
`:'N^(r)=(x+1/x)^(6)-(x^(6)+1/(x^(6)))-2`
`=(x+1/x)^(6)=(x^(3)+1/(x^(3)))^(2)=((x+1/x)^(3)+(x^(3)+1/(x^(3))))`
`((x+1/x)^(3)-(x^(3)+1/(x^(3))))`
`=D^(r).(3(x+1/x))`
`:.(N^(r))/(D^(r))=3(x+1/x)ge6`
Hence minimum value of `(N^(r))/(D^(r))` is 6.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2)) , where |x|<1/(sqrt(3)) . Then a value of y is : (1) (3x-x^3)/(1-3x^2) (2) (3x+x^3)/(1-3x^2) (3) (3x-x^3)/(1+3x^2) (4) (3x+x^3)/(1+3x^2)

Find the sum of (x + (1)/(x))^(2), (x^(2) + (1)/(x^(2)))^(2), (x^(3) + (1)/(x^(3)))^(2) , ……..to n terms

If the x= 5 +2sqrt6 find the value of x^(2) + (1)/(x^(2)) and x^(3) + (1)/(x^(3))

If x=sqrt(2)-1 then find the value of ((1)/(x)-x)^(3) :-

The value of p(x) = x^(3) + x^(2) - 3x-3 at x = -1 is …… .

Find absolute maximum and minimum values of a function f given by f(x)=12x^((4)/(3))-6x^((1)/(3)), x in [-1, 1]

For all real values of x, the minimum value of f(x)=(1-x+x^(2))/(1+x+x^(2)), AA x in R is ……….

Find value of (x+(1)/(x))^(3)+(x^(2)+(1)/(x^(2)))^(3)+"........"+(x^(n)+(1)/(x^(n)))^(3) .

If |{:(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x):}| =3 then the value of |{:(x^(3)-1,0,x-x^(4)),(0,x-x^(4),x^(3)-1),(x-x^(4),x^(3)-1,0):}| is