[tex]x = 3 + 2 \sqrt{2} [/tex]
Find the value of x³-1/x³
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[tex]x = 3 + 2 \sqrt{2} [/tex]
Find the value of x³-1/x³
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Answer:
Given x= 3+2√2
we have to find the value of
[tex] {x}^{3} - \frac{1}{ {x}^{3} } [/tex]
first
1/x = 1/3+2√2
rationalizing the denominator
[tex] = \frac{3 - 2 \sqrt{2} }{(3 + 2 \sqrt{2}) (3 - 2 \sqrt{2}) } \\ = \frac{3 - 2 \sqrt{2} }{9 - 8} = 3 - 2 \sqrt{2} [/tex]
now
x-1/x
=3+2√2-(3-2√2 )
=4√2
we know the algebraic identity which tells us
[tex] {a}^{3} - {b}^{3} = {(a - b)}^{3} + 3ab(a - b)[/tex]
now ,
[tex] {x}^{3} - \frac{1}{ {x}^{3} } \\ = {(4 \sqrt{2} )}^{3} + 3(4 \sqrt{2} ) \\ = 128 \sqrt{2} + 12 \sqrt{2} = 140 \sqrt{2} [/tex]
hope it helps you
Answer:
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