Math, asked by kowshik000, 1 day ago


please \: solve \:   \\  \\ x +  \frac{1}{x}  = 9 \: then \: find \: the \: value \: of \:  \\  {x}^{4} +  \frac{x}{ {x}^{4} }
Please solve this

Answers

Answered by Dalfon
57

Answer:

6239

Step-by-step explanation:

Given: x + 1/x is 9. We need to find out the value of x⁴ + 1/x⁴.

Now,

→ x + 1/x = 9

Do squaring on both sides,

→ (x + 1/x)² = (9)²

→ x² + 1/x² + 2x(1/x) = 81

Used formula: (a + b)² = a² + b² + 2ab

→ x² + 1/x² + 2 = 81

→ x² + 1/x² = 81 - 2

→ x² + 1/x² = 79

Hence, the value of x² + 1/x² is 79. But we need to find out the value of x⁴ + 1/x⁴. While squaring on x + 1/x we get the value of x² + 1/x². If we do squaring on x² + 1/x² then we'll get the value of x⁴ + 1/x⁴.

→ x² + 1/x² = 79

Do squaring again,

→ (x² + 1/x²)² = (79)²

→ x⁴ + 1/x⁴ + 2(x²)(1/x²) = 6241

→ x⁴ + 1/x⁴ + 2 = 6241

→ x⁴ + 1/x⁴ = 6241 - 2

→ x⁴ + 1/x⁴ = 6239

Therefore, the value of x⁴ + 1/x⁴ is 6239.

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