Question

solve this..........................Q-12

Answer 1

if x^4 + 1 / x^4 = 119 , then x - ( 1 / x ) = ?

solve for (x-1/x) :
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using identities :
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(1) a^2+ b^2 +2ab = ( a + b)^2

(2) a^2 + b^2 - 2ab = ( a - b)^2
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x^4 + 1/x^4 = 119

(x^2)^2 + (1/x^2)^2 + 2(x^2)(1/x^2) - 2(x^2) (1/x^2) = 119

( x^2 + 1/x^2 )^2 - 2 (x^2) (1 /x^2) = 119

(x^2 + 1/x^2 )^2 - 2 = 119

(x^2 + 1/x^2)^2 = 119 + 2

(x^2 + 1/x^2)^2 = 121

(x^2 + 1/x^2) = √121

( x^2 + 1/x^2 ) = 11

( x )^2 + (1/x )^2 + 2(x)(1/ x) - 2(x)(1/x) = 11

( x - 1/x )^2 + 2 (x ) ( 1/ x ) = 11

( x - 1/x )^2 + 2 = 11

( x - 1/x )^2 = 11 - 2

( x - 1/x )^2 = 9

x - 1/x = √9

x - 1/x = 3

therefore , value of ( x - 1/ x ) = 3

Answer : 3

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