if x=3+√8 then the value of x²+1/x² is
Answers
Answered by
1
Answer:
34
Step-by-step explanation:
Given that..
x=3+8–√…(1)
⇒1x=3−8√(3)2−(8√)2
⇒1x=3−8–√….(2)
Now adding (1) & (2) we get…
x+1x=(3+8–√)+(3−8–√)
⇒x+1x=6
Now,
x2+1x2
=(x+1x)2–2.x1x
=62–2
=36–2
=34 . (Ans).
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Answered by
4
EXPLANATION.
⇒ x = 3 + √8.
As we know that,
We can write equation as,
Multiply and divide by 3 - √8 in equation, we get.
⇒ x = (3 + √8)(3 - √8)/(3 - √8).
⇒ x = [(3)² - (√8)²]/(3 - √8).
⇒ x = (9 - 8)/(3 - √8).
⇒ x = 1/(3 - √8).
⇒ x[(3 - √8)] = 1.
⇒ 1/x = 3 - √8.
⇒ x + 1/x.
⇒ (3 + √8) + (3 - √8).
⇒ 3 + √8 + 3 - √8 = 6.
⇒ (x² + 1/x²) = (x + 1/x)² - 2(x)(1/x).
⇒ (x² + 1/x²) = (6)² - 2.
⇒ (x² + 1/x²) = 36 - 2.
⇒ (x² + 1/x²) = 34.
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