Question

find the value of this question​

Answer 1

Answer:

x² + 1 / x² = 10 and x⁴ + 1 / x⁴ = 98

Step-by-step explanation:

Given---> x - 1 / x = √8

To find ---> x² + 1 / x² = ? , x⁴ + 1 / x⁴ = ?

Solution---> We have two identities

( a - b )² = a² + b² - 2 a b

(a + b )² = a² + b² + 2 a b

ATQ, x - 1 / x = √8

Squaring both sides , and using first identity written above , we get

=> ( x - 1 / x )² = ( √8 )²

=> x² + ( 1 / x )² - 2 ( x ) ( 1 / x ) = 8

=> x² + 1 / x² - 2 = 8

=> x² + 1 / x² = 8 + 2

=> x² + 1 / x² = 10

Squaring both sides again and using second identity written above, we get

=> ( x² + 1 / x² )² = ( 10 )²

=> ( x² )² + ( 1 / x² )² + 2 ( x² ) ( 1 / x² )² = 100

=> x⁴ +( 1 / x⁴ ) + 2 = 100

=> x⁴ + 1 / x⁴ = 100 - 2

=> x⁴ + 1 / x⁴ = 98