Question

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Question is in the attachment

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Answer 1

Answer:-

Given:

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

Let a = x and b = 1/x.

Let us find ab = x(1/x)

→ ab = 1.

We know that,

(a - b)² = (a + b)² - 4ab

→ (x - 1/x)² = (2)² - 4

→ (x - 1/x)² = 0

→ x - 1/x = 0 -- equation (2).

Adding both the equations we get,

→ x + 1/x + x - 1/x = 2 + 0

→ 2x = 2

→ x = 2/2

→ x = 1.

Now finding the value of x² + 1/x²,

→ (1)² + 1/(1)²

→ 1 + 1

→ 2

Similarly finding x³ + 1/x³,

→ (1)³ + 1/(1)³

→ 1 + 1

→ 2

Now finding x⁴ + 1/x⁴,

→ (1)⁴ + 1/(1)⁴

→ 1 + 1

→ 2

Hence, x² + 1/x² = x³ + 1/x³ = x⁴ + 1/x⁴.

Answer 2

Answer in attachment

Hope it helps