Question
.If a = `sqrt(11+2sqrt18` and b
= `sqrt(11-2sqrt18)` , what is the value of a³ + b³?Solution
Given a =`sqrt(11+2sqrt18)` = `sqrt(9+2+2*3sqrt2)` =`sqrt((3+sqrt2)^2)` =`3+sqrt2` Similarly b = `3-sqrt2` ∴ a + b = (3 + √2) + (3 - √2) = 6 a * b = (3 + √2) * (3 - √2) = 9 - 2 = 7 a³ + b³ = (a + b)³ - 3ab(a + b) ⇒ a³ + b³ = 6³ - 3 * 7 * 6 = 216 - 126 ⇒ a³ + b³ = 90
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