Home
Class 10
MATHS
If (9+4sqrt(5))^x+(9-4sqrt(5))^x=18 the...

If `(9+4sqrt(5))^x+(9-4sqrt(5))^x=18` then the value of `x^2-1/(x^2)`

Text Solution

Verified by Experts

`(9+4sqrt5)^x+(9-4sqrt5)^x = 18`
When `x = 1`,
`9+4sqrt5+9-4sqrt5 = 18`
So, this equation is true for `x = 1`.
Putting `x=1`, in the desired expression,
`:. x^2-1/x^2 = 1-1/1 = 1-1 = 0`
Promotional Banner

Similar Questions

Explore conceptually related problems

(9+4sqrt(5))^(x)+(9-4sqrt(5))^(x)=18, then find x^(2)-(1)/(x^(2))

If x = 9 - 4sqrt(5) , find the value of x^(2) +(1)/(x^(2)) .

sqrt(2)x^(2)+9x+4sqrt(2)

If x=9−4sqrt5 then , find the value of [x^3− 1/(x^3)]

If , 4x = sqrt5+2 , then the value of (x-1/(16x)) is

If x=sqrt((sqrt(5)+1)/(sqrt(5)-1)), then the value of x= of 5x^(2)-5x-1 is

if x=9+4sqrt(5) find the value of sqrt(x)-(1)/(sqrt(x))