Question

X raise to power 4 + 1 upon x raise to power 4 equals to 322 find the value of x minus one upon x

Answer 1

Answer :

Given,

x⁴ + 1/x⁴ = 322

⇒ (x² + 1/x²)² - (2 × x² × 1/x²) = 322

⇒ (x² + 1/x²)² - 2 = 322

⇒ (x² + 1/x²)² = 324

⇒ x² + 1/x² = √324, taking the positive value

⇒ x² + 1/x² = 18

⇒ (x - 1/x)² + (2 × x × 1/x) = 18

⇒ (x - 1/x)² = 18 - 2

⇒ (x - 1/x)² = 16

⇒ x - 1/x = ± 4

Thus, x - 1/x = ± 4

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Answer 2

x⁴ + 1/x⁴ = 322

Adding 2 [ x² × 1/x²] on both sides,

x⁴ + 1/x⁴ + 2 [x² × 1/x⁴] = 322 + 2 [x² × 1/x²]


=> (x² + 1/x²)² = 324

=> x² + 1/x² = √324

=> x² + 1/x² = 18

Adding -2 [x × 1/x] on both sides,

=> x² + 1/x² - 2 [x × 1/x] = 18 - 2 [x × 1/x]

=> (x - 1/x)² = 18 - 2

=> (x - 1/x)² = 16

=> x - 1/x = 4 [your answer]


I hope this will help you


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