Question

Evaluate (1+√2)³+(1-√2)³

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Answer 1

14

Explanation:

Answer 2

14

Explanation:

Evaluate

`(1+√(2))^3 + (1-√(2))^3`

As we have the Cube binomials:

`\boxed{(a+b)^3=a^3+3a^2b+3ab^2+b^3}`

`\boxed{(a-b)^3=a^3-3a^2b+3ab^2-b^3}`

`(1+√(2))^3 =1^3 + 3\cdot 1^2 \cdot√(2) + 3 \cdot 1 \cdot (√(2)) ^2 + (√(2)) ^3 = \boxed{7+5√(2)}`

`(1-√(2))^3 =1^3 - 3\cdot 1^2 \cdot√(2) + 3 \cdot 1 \cdot (√(2)) ^2 - (√(2)) ^3 = \boxed{7-5√(2)}`

`\therefore (1+√(2))^3 + (1-√(2))^3 =7+5√(2) + 7-5√(2) = \boxed{14}`