if x=1-root 2 , find (x-1/x)cube
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0
(x-1/x)^3
(1-√2-1/1-√2)^3
(-√2/1-√2)^3
-2√2/1-2√2
= -2√2-8/-7
(1-√2-1/1-√2)^3
(-√2/1-√2)^3
-2√2/1-2√2
= -2√2-8/-7
Answered by
2
Hi friend,
x = 1-√2
1/x = 1/1-√2
= 1/1-√2 × 1+√2/1+√2
= (1+√2)/(1-√2)(1+√2)
= (1+√2)/(1²-√2²)
= (1+√2)/(1-2)
= -(1+√2)
= -1-√2
(x-1/x)³
=> [1-√2-(-1-√2)]³
=> [1-√2+1+√2]³
=>2³
=> 8
Therefore, (x-1/x)³ = 8
Hope it helps
x = 1-√2
1/x = 1/1-√2
= 1/1-√2 × 1+√2/1+√2
= (1+√2)/(1-√2)(1+√2)
= (1+√2)/(1²-√2²)
= (1+√2)/(1-2)
= -(1+√2)
= -1-√2
(x-1/x)³
=> [1-√2-(-1-√2)]³
=> [1-√2+1+√2]³
=>2³
=> 8
Therefore, (x-1/x)³ = 8
Hope it helps
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