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Q.

The value of x 2 + 1 x 2   if x+ 1 x =4,   is ____.


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Detailed Solution

The value of x 2 + 1 x 2   if x+ 1 x =4,   is 14.
Here, we have to find the value of x 2 + 1 x 2    if x+ 1 x =4  .
We know that,
(x+y) 2 = x 2 + y 2 +2xy  
Squaring on both sides of x+ 1 x =4  , we get,
⇒ x+ 1 x 2 = x 2 + 1 x 2 +2(x) 1 x   ⇒ x+ 1 x 2 = x 2 + 1 x 2 +2  ………………….(1)
Put x+ 1 x =4  in equation (1). We get,
4 2 = x 2 + 1 x 2 +2   ⇒16= x 2 + 1 x 2 +2  
⇒16−2= x 2 + 1 x 2  
⇒ x 2 + 1 x 2 =14   Hence, the value of  x 2 + 1 x 2 =14  .
 
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The value of x 2 + 1 x 2   if x+ 1 x =4,   is ____.