Question

if x=3+√8 then the value of x²+1/x² is​

Answer 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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Answer 2

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.