Question
.If a = `sqrt(11+2sqrt18` Â Â 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
More Simplification Questions
√323.89  × (3.20) ÷ 9.02 =?
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
23.98% of 624.99 = 19.98% of ? + 14.98% of 639.99
Direction: Please solve the following expression and choose the closest option
What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)...
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
12, 16, ?, 36, 52, 72Â
- What approximate value will come in place of the question mark (?) in the following question? (Note: You are not expected to calculate the exact value.)
(6859.01)1/3  × 10.11 × 14.47 ÷ 20.32 = ? + 45.022
33.33% of 809.891 + 66.66% of 212.91 = ?
