If x+1/x=7 then find the value of x3 +1/x3

X +1/X = 7

(X + 1/X)3 = 73

X3 + 1/X3 + 3 X (1/X) (X+ 1/X) = 343          As, ( a+ b)3 = a3+ b3+3ab(a+b)

X3+ 1/X3+ 3*7 = 343

X3+ 1/X3 =343−21

X3+ 1/X3= 322

  • 70

x3 + 1/x3 =x3 + (1/x)3

a3 + b3 = (a + b) ( a2 + ab + b2 ) - IDENTITY

In the above question

a = x3

b = (1/x)3

x3+ (1/x)3= { x + (1/x) } { x2 + (x)(1/x) + (1/x)2 }Given that x + 1/x = 7

=(7) { x2+ (x/x) + 1/x2}

= (7) { x2+ 1 + 1/x2}

= 7x2 + 7 + 7/x2 --ANSWER

  • -1
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