If x-x-1-11- evaluate x2-x-2A- 119B- 120C- 121D- 122

The correct option is A 119x + x^ 1 nbsp;= 11 (x + x^ 1)^2 nbsp;= 11^2 nbsp; [Squaring both the sides] ⇒(x)^2 + (x^ 1)^2 + 2(x)(x^ 1) = 121 ⇒ x^2 + x^ 2 ...

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Standard X

Mathematics

Composition of Function

If x+x-1=11, ...

Question

If $x + x^{- 1} = 11$ , evaluate $x^{2} + x^{- 2}$ .

119

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Solution

The correct option is A 119
$x + x^{- 1} = 11$

$({x + x^{- 1})}^{2} = 11^{2}$ [Squaring both the sides]

$\Rightarrow {(x)}^{2} + {(x^{- 1})}^{2} + 2 (x) (x^{- 1}) = 121$

$\Rightarrow x^{2} + x^{- 2} + 2 = 121$ $[∵ (x) (x^{- 1}) = x^{0} = 1]$

$\Rightarrow x^{2} + x^{- 2} = 121 - 2 = 119$

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If x+x−1=11, evaluate x2+x−2.

The correct option is A 119x+x−1=11 (x+x−1)2=112 [Squaring both the sides] ⇒(x)2+(x−1)2+2(x)(x−1)=121 ⇒ x2+x−2+2=121 [∵(x)(x−1)=x0=1] ⇒ x2+x−2=121−2=119

If $x + x^{- 1} = 11$ , evaluate $x^{2} + x^{- 2}$ .

The correct option is A 119
$x + x^{- 1} = 11$

$({x + x^{- 1})}^{2} = 11^{2}$ [Squaring both the sides]

$\Rightarrow {(x)}^{2} + {(x^{- 1})}^{2} + 2 (x) (x^{- 1}) = 121$

$\Rightarrow x^{2} + x^{- 2} + 2 = 121$ $[∵ (x) (x^{- 1}) = x^{0} = 1]$

$\Rightarrow x^{2} + x^{- 2} = 121 - 2 = 119$