if x=3+2√2 find the value of √x-1/√x)^3
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Answer:
the value of (√x-1/√x)^3 is 8.
Step-by-step explanation:
Given :
If x=3+2√2
To find :
the value of (√x-1/√x)^3
Solution :
= (√x-1/√x)^3
=[√(3+2√2) -1/√(3+2√2) ]^3
As √(3+2√2) = √2+1
Thus we get,
=[(√2+1 ) -1/(√2+1 ) ]^3
=[(√2+1 ) -(√2-1) ]^3
=[√2+1 -√2+1 ) ]^3
=[+1 +1 ) ]^3
=2^3
=8
And : Hence, the value of
(√x-1/√x)^3 is 8.
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