Math, asked by Mister360, 2 months ago

If (x² + 1/x²) = 38 then find
1. x - 1/x

2. x⁴ + 1/x⁴

Answers

Answered by farhaanaarif84
0

Answer:

x−

x

1

We have,

(x−

x

1

)

2

=x

2

−2×x×

x

1

+

x

2

1

⇒(x−

x

1

)

2

=x

2

−2+

x

2

1

⇒(x−

x

1

)

2

=x

2

+

x

2

1

−2

⇒(x−

x

1

)

2

=27−2[∵x

2

+

x

2

1

=27 given]

⇒(x−

x

1

)

2

=25⇒(x−

x

1

)

2

⇒x−

x

1

=±5

[Taking square root of both sides]

Answered by anindyaadhikari13
4

Required Answer:-

Given:

  • x² + 1/x² = 38.

To Find:

  • x - 1/x = ?
  • x⁴ + 1/x⁴ = ?

Formulae To Be Used:

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

Solution:

Given that,

➡ x² + 1/x² = 38

Subtracting 2 from both sides, we get,

➡ x² + 1/x² - 2 = 38 - 2

➡ (x)² + (1/x)² - 2 × (x) × (1/x) = 36

Now, this is in (a - b)² form. So,

➡ (x - 1/x)² = 36

➡ x - 1/x = ±√36

➡ x - 1/x = ±6

Hence, x - 1/x = ±6

Again,

➡ x² + 1/x² = 38

Squaring both sides, we get,

➡ (x²)² + (1/x²)² + 2 × (x²) × (1/x²) = 1444

➡ x⁴ + 1/x⁴ + 2 = 1444

➡ x⁴ + 1/x⁴ = 1442

Hence, x⁴ + 1/x⁴ = 1442

Answer:

  • x - 1/x = ±6
  • x⁴ + 1/x⁴ = 1442.
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