Question

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Answer 1

Answer:

x⁵ + (1/x⁵) = 2

Step-by-step explanation:

Now, we are given,

√x + (1/√x) = 2

Squaring both sides we get,

(√x + (1/√x))² = 2²

(a + b)² = a² + 2ab + b²

(√x)² + (2 × √x × (1/√x)) + (1/√x)² = 4

x + 2 + (1/x) = 4

x + (1/x) = 4 - 2

x + (1/x) = 2 ------- 1

Now,

(x + (1/x))² = 2²

(a + b)² = a² + 2ab + b²

x² + (2 × x × (1/x)) + (1/x)² = 4

x² + 2 + (1/x²) = 4

x² + (1/x²) = 4 - 2

x² + (1/x²) = 2 ------ 2

Now,

(x + (1/x))³ = 2³

(a + b)³ = a³ + 3ab(a + b) + b³

x³ + (3 × x × (1/x))(x + (1/x)) + (1/x)³ = 8

From eq.1,

x³ + (3(2)) + (1/x³) = 8

x³ + 6 + (1/x³) = 8

x³ + (1/x³) = 8 - 6

x³ + (1/x³) = 2 ------- 3

Multiplying eq.2 and eq.3 we get,

(x² + (1/x²))(x³ + (1/x³)) = 2 × 2

x⁵ + (1/x) + x + (1/x⁵) = 4

x⁵ + (1/x⁵) + x + (1/x) = 4

x⁵ + (1/x⁵) + (x + (1/x)) = 4

From eq.1,

x⁵ + (1/x⁵) + 2 = 4

x⁵ + (1/x⁵) = 4 - 2

∴ x⁵ + (1/x⁵) = 2

Hope it helped and believing you understood it........All the best

Answer 2

Answer:

Congratulations DEAR ❣️❣️