if x + 1/x = 9 find the value of x3 + 1/x3
Answers
Answered by
27
given
x + 1/x = 9
x + 1 = 9x
1 = 9x - x
1/8 = x
Now
x^3 + 1 / x^3
(1/8)^3 + 1/(1/8)^3
= (1/512 + 1)/(1/512)
= ((1 + 512)/512)/1/512
= 513
x + 1/x = 9
x + 1 = 9x
1 = 9x - x
1/8 = x
Now
x^3 + 1 / x^3
(1/8)^3 + 1/(1/8)^3
= (1/512 + 1)/(1/512)
= ((1 + 512)/512)/1/512
= 513
Answered by
21
x+1/x=9
squaring both side
x2+1/x2+2×1/x2×x2=(9)2
x2+1/x2=81-2=79
Multiply first and second equation
(x+1/x)(1/x2+x2)=79
x3+x+1/x+1/x3=79
x3+1/x3+(x+1/x)=79
x3+1/x3+9=79
x3+1/x3=79-9=70
squaring both side
x2+1/x2+2×1/x2×x2=(9)2
x2+1/x2=81-2=79
Multiply first and second equation
(x+1/x)(1/x2+x2)=79
x3+x+1/x+1/x3=79
x3+1/x3+(x+1/x)=79
x3+1/x3+9=79
x3+1/x3=79-9=70
SakshaM725:
if you multiply equation one and two then 79 is also multiplied by 9
and please mention equation 1 and two
I forget multiplying. correct it
ok
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