Question

If x² + 1 /81ײ = 2, find 3× - 1/3× and 81×⁴ + 1/81×⁴​

Answer 1

Step-by-step explanation:

x² + 1/81x²

= (x - 1/9x)² + 2/9

or, 2 = (x - 1/9x)² + 2/9

or, 2-2/9 = (x-1/9x)²

or, 16/9 = (x-1/9x)²

or, √16/√9 = x-1/9x

or, 4/3 = x-1/9x

or, 4 = 3x - 1/3x

or, 3x - 1/3x = 4

81x⁴ + 1/81x⁴

= {9x² + 1/9x²}² - 2

= {(3x - 1/3x)² + 2}² - 2

= {4² + 2}² - 2

= 18² - 2

= 324 - 2

= 322