If x2 + 1/x2 = 79, find the value of x2 -1/x2
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SQUARING BOTH SIDES
(x² + 1/x²) ² = (79)²
X⁴ + 1/X⁴ + 2 = (79)² ---------- (2)
NOW a²+b²= (a-b)² + 2ab, using this identity in equation (2)
(x² - 1/x²)² + 2(x²)(1/x²) + 2 = 6241
(x² - 1/x²)² = 6241-4
(x² - 1/x²)² = 6237 ------- ANSWER
(x² + 1/x²) ² = (79)²
X⁴ + 1/X⁴ + 2 = (79)² ---------- (2)
NOW a²+b²= (a-b)² + 2ab, using this identity in equation (2)
(x² - 1/x²)² + 2(x²)(1/x²) + 2 = 6241
(x² - 1/x²)² = 6241-4
(x² - 1/x²)² = 6237 ------- ANSWER
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