Question

pls answer this question !!!! !!!​

Answer 1

Answer:

here's your answer dear

Answer 2

Question:-

If x - 1/x = 10 (where x is a positive integer) then find;

a) x² + 1/x²

b) x + 1/x

c) x² - 1/x²

Answer:-

1) Given:-

x - 1/x = 10

On squaring both sides we get,

⟹ (x - 1/x)² = (10)²

using (a - b)² = a² + b² - 2ab we get,

⟹ x² + 1/x² - 2(x)(1/x) = 100

⟹ x² + 1/x² = 100 + 2

⟹ x² + 1/x² = 102

∴ The value of x² + 1/x² is 102.

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2) We have;

x² + 1/x² = 102

We know,

a² + b² = (a + b)² - 2ab

So,

⟹ x² + 1/x² = (x + 1/x)² - 2(X)(1/X)

⟹ 102 = (x + 1/x)² - 2

⟹ 102 + 2 = (x + 1/x)²

⟹ 104 = (x + 1/x)²

⟹ √104 = (x + 1/x)

⟹ 2√26 = x + 1/x

∴ The value of x + 1/x is 2√26.

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3) We have;

x + 1/x = 2√26 -- equation (1)

x - 1/x = 10 -- equation (2)

Multiply equations (1) & (2).

⟹ (x + 1/x)(x - 1/x) = (2√26)(10)

using (a + b)(a - b) = a² - b² we get;

⟹ x² - 1/x² = 20√26

∴ The value of x² - 1/x² is 20√26.