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Let a and b be the roots of the equation 2x^2 - 7x + 2 = 0. Find 1/(a-1)+1/(b-1)

 Jun 24, 2023
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The roots of the equation 2x^2 - 7x + 2 = 0 are

a = (7 + sqrt(7^2 - 4 * 2 * 2)) / 4 = 4 + sqrt(3) b = (7 - sqrt(7^2 - 4 * 2 * 2)) / 4 = 4 - sqrt(3)

Therefore,

1/(a-1) + 1/(b-1) = (1/(4-sqrt(3)) + 1/(4+sqrt(3))) = (4 + sqrt(3) + 4 - sqrt(3)) / (16 - 3) = 8 / 13 = \boxed{8/13}

 Jun 24, 2023

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