Home
Class 12
MATHS
Evaluate the following: \ (x+sqrt(x^2-1)...

Evaluate the following: `\ (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6`

Text Solution

Verified by Experts

Let
Then , `(x+ a)^(6) + (x - a)^(6) = 2 {""^(6)C_(0) x^(6-0) a^(0) + ""^(6)C_(2) + x^(6-2) a^(2) + ""^(6)C_(4) x^(6-4) a^(4) + ""^(6)C_(6) x^(6-6) a^(4)}`
`= 2 {x^(6) + 15x^(4) a^(2) + 15x^(2) + 15x^(2) a^(4) + a^(6)} " " ` [from point (2)]
`= 2 {x^(6) 15x^(4) (x^(2) -1) + 15 x^(2) (x^(2) -1)^(2) + (x^(2) -1)^(3)} " " [ because a = sqrt(x^(2) -1)]`
` = 2(32 x^(6) - 48 x^(6) - 48x^(4) + 18x^(2) -1)` .
Promotional Banner

Similar Questions

Explore conceptually related problems

Evaluate the following integration int(dx)/(sqrt(x+1)-sqrt(x))

(x+1) sqrt(2x^(2)+3)

Integrate the following function : int(x^(2))/(sqrt(x^(6)-1))dx

Evaluate the following integrals : int_(1/4)^(1/2)(dx)/(sqrt(x-x^(2)))

Find (dy)/(dx) in the following: y= sin^(-1) (2x sqrt(1-x^(2))), (1)/(sqrt2) lt x lt 1

Find (dy)/(dx) in the following y= sin^(-1) (2x sqrt(1-x^(2))), -(1)/(sqrt2) lt x lt (1)/(sqrt2)

Solve the following equations: x^(2)-(3 sqrt(2)+2i)x+6 sqrt(2)i=0

Solve sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=1

Find the domain of f(x)=sqrt(1-sqrt(1-sqrt(1-x^2)))

Prove the following : sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,x in[-1/sqrt2,1/sqrt2]