If x = 3 - 2√2 ,then find the value of x - 1/x *
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Your answer is (- 14 - 14√2).
Step-by-step explanation:
Given that x = 3 - 2√2
Then 1/x = 1/3 - 2√2
=1(3 + 2√2)/(3 - 2√2)(3 + 2√2)
=3 + 2√2/3² - (2√2)²
=3 + 2√2/9 - 8
=3 + 2√2/1
=3 + 2√2
⇒1/x² = (3 + 2√2)²
=3² + 2 × 3 × 2√2 + (2√2)²
=9 + 12√2 + 8
=17 + 12√2
∴ x - 1/x² = 3 - 2√2 - (17 + 12√2)
= 3 - 2√2 - 17 - 12√2
= (- 14 - 14√2)
hope it helps
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