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Answered by
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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