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How do you find the formula of infinite surds? - Answers

x =√k+√k+√k…… ectx² = k + xx² - x = kx² - x + (1/2)² = k + (1/2)² factorise x² - x + (1/2)²(x + 1/2)² = k + 1/4(x + 1/2)² = (4k + 1)/4x + 1/2 = ± √(4k + 1)/2x = 1/2 ± √(4k + 1)/2it obviously has to be positivex = 1/2 + √(4k + 1)/2x = (1 + √(4k + 1))/2



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How do you find the formula of infinite surds? - Answers

https://math.answers.com/algebra/How_do_you_find_the_formula_of_infinite_surds

x =√k+√k+√k…… ectx² = k + xx² - x = kx² - x + (1/2)² = k + (1/2)² factorise x² - x + (1/2)²(x + 1/2)² = k + 1/4(x + 1/2)² = (4k + 1)/4x + 1/2 = ± √(4k + 1)/2x = 1/2 ± √(4k + 1)/2it obviously has to be positivex = 1/2 + √(4k + 1)/2x = (1 + √(4k + 1))/2



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https://math.answers.com/algebra/How_do_you_find_the_formula_of_infinite_surds

How do you find the formula of infinite surds? - Answers

x =√k+√k+√k…… ectx² = k + xx² - x = kx² - x + (1/2)² = k + (1/2)² factorise x² - x + (1/2)²(x + 1/2)² = k + 1/4(x + 1/2)² = (4k + 1)/4x + 1/2 = ± √(4k + 1)/2x = 1/2 ± √(4k + 1)/2it obviously has to be positivex = 1/2 + √(4k + 1)/2x = (1 + √(4k + 1))/2

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      x =√k+√k+√k…… ectx² = k + xx² - x = kx² - x + (1/2)² = k + (1/2)² factorise x² - x + (1/2)²(x + 1/2)² = k + 1/4(x + 1/2)² = (4k + 1)/4x + 1/2 = ± √(4k + 1)/2x = 1/2 ± √(4k + 1)/2it obviously has to be positivex = 1/2 + √(4k + 1)/2x = (1 + √(4k + 1))/2

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