If x+ 1 x =9, find the value of x 2 + 1 x 2 .

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If $x + 1 x = 9,$ find the value of $x 2 + 1 x 2$ .

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100

answer is A.

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Detailed Solution

Given expression is

x + 1 x = 9

.
Using the identities,

a + b 2 = a 2 + b 2 + 2 a b

Consider, a=x and b=

\frac{1}{x}

x + 1 x 2 = x 2 + 1 x 2 + 2 × x × 1 x ⇒ 92 = x 2 + 1 x 2 + 2 ⇒ 81 = x 2 + 1 x 2 + 2 ⇒ x 2 + 1 x 2 = 81 − 2 ⇒ x 2 + 1 x 2 = 79

Therefore, the value of

x 2 + 1 x 2

is 79.
Hence, option 1 is correct.

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