Question

if a + 1 upon a equals to under root 5 find the value of 1 upon a power 4 + a power 4

Answer 1

Hello !!

A + 1/A = ✓5



On squaring both sides , we get ;


( A + 1/A)² = (✓5)²

A² + 1/A² + 2 × A × 1/A = 5

A² + 1/A² + 2 = 5

A² + 1/A² = 5-2

A² + 1/A² = 3


On squaring both sides , we get ;


★ ( A² + 1/A²)² = (3)²

=> A⁴ + 1/A⁴ + 2 × A² × 1/A² = 9

=> A⁴ + 1/A⁴ + 2 = 9

=> A⁴ + 1/A⁴ = 9-2

=> A⁴ + 1/A⁴ = 7

Hence,

1/A⁴ + A⁴ = 7.

Answer 2

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