Question

please answer the question given below
...if the answer is correct then you'll be marked as brainliest....at least try...BTW the answer is 12 but I need the whole solution....pls​

Answer 1

Answer:

Hey !

Step-by-step explanation:

Given : 2019^x+2019^-x=3

To Find : value of

12019^6x-2019^-x=2019^x-2019^-X

2019^x+2019^-x=3

Let say 2019^x = a

=> 2019^-x = 1/a

a + 1/a = 3

=> a² + 1 = 3a

(√2019^6x-2019^-x)÷ (2019^x-2019^-x)

=  (2019^3x - 2019^-x)÷ (2019^x-2019^-x)

= ( a³ - 1/a) ÷ (a -1/a)

multiplying numerator and denominator by a

= ( a⁴ - 1)  ÷ (a² - 1)

= (a² + 1)(a² - 1)  ÷ (a² - 1)

= a² + 1

= 3a

 

a² + 1 = 3a

=> a² - 3a + 1 = 0

=> a  = (3 ± √9-4)/2

=> a = (3 ± √5)/2

√2019^6x-2019^-x÷2019^x-2019^-x =   3  (3 ± √5)/2

I Hope it helps You ❤