given x + 1/x = 6
squaring both sides
(x + 1/x)² = 6²
x² + 1/x² + 2 ×x× 1/x = 36
x² + 1/x² + 2 = 36
x²+ 1/x² = 36 - 2
x² + 1 /x² = 34
(x - 1/x)² = x² +1/x² - 2×x×1/x
(x - 1/x)² = 34 - 2
(x - 1 /x)² = 32
x - 1/x = +√32
x - 1/x = +√2×2×2×2×2
x - 1/x = + 4√ 2
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Answers & Comments
given x + 1/x = 6
squaring both sides
(x + 1/x)² = 6²
x² + 1/x² + 2 ×x× 1/x = 36
x² + 1/x² + 2 = 36
x²+ 1/x² = 36 - 2
x² + 1 /x² = 34
(x - 1/x)² = x² +1/x² - 2×x×1/x
(x - 1/x)² = 34 - 2
(x - 1 /x)² = 32
x - 1/x = +√32
x - 1/x = +√2×2×2×2×2
x - 1/x = + 4√ 2