Question

if a²-1/a²=5 then find a⁴+1/a⁴​

Answer 1

Answer:

27

Step-by-step explanation:

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Answer 2

Given

if a²-1/a²=5 then find a⁴+1/a⁴

To find

a⁴ + 1/a⁴

Solution

a² - 1/a² = 5

squaring both side

=> (a² - 1/a²)² = (5)²

=> a⁴ + 1/a⁴ - 2 × a² × 1/a² = 25

=> a⁴ + 1/a⁴ - 2 = 25

=> a⁴ + 1/a⁴ = 25 + 2

=> a⁴ + 1/a⁴ = 27

Some important identities

• (a+b)² = a² + b² + 2ab
• (a-b)² = a² + b² - 2ab
• (a+b)³ = a³ + b³ + 3ab(a+b)
• (a-b)³ = a³ - b³ - 3ab(a-b)
• a² - b² = (a+b)(a-b)
• a³ - b³ = (a-b)(a²+ab+b²)
• a³ + b³ = (a+b)(a² -ab +b²)