Question

if x²+1/x²=102 then x-1/x

Answer 1

since

(x-1/x)²=x²+1/x²-2,


then

(x-1/x)²=102-2,


(x-1/x)²=100,

then

(x-1/x)=√100,


x-1/x=10

Answer 2

x² + 1 / x² = 102



First, spitting 102 in two numbers, but one number should be 2 because we have to apply the formula ( a - b )² = a² + b² - 2ab. So :-



x² + 1 / x² = 100 + 2

x² + 1 / x² - 2 = 100



We can 2 as 2 × 1 because it produces no change as 2 and 2 × 1 are same.



x² + 1 / x² - 2( 1 ) = 100



if divide x by x, we get 1 . so now putting x divided by x in place of 1 ,



x² + 1 / x² - 2( x / x ) = 100



We can write x / x as x × 1 / x ,



x² + 1 / x² - 2( x × 1 / x ) = 100



Now using the indentity , a² + b² - 2ab = ( a - b )²



( x - 1 / x )² = 100

x - 1 / x = √100

x - 1 / x = ± 10



Therefore the value of x - 1 / x is + 10 or - 10. But usually we put the positive value so,



x - 1 / x = 10

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