if x-1/x=√3 find the value of (x^2+1/x^2)(x^3+1/x^3)
Answers
Answered by
0
Step-by-step explanation:
It is given that,
x−1/x−3+2
2
So,
x
3
−1/x
3
=(x−1/x)
3
+3(x−1/x)
=(3+2
2
)
3
+3(3+2
2
)
By using the formula, (a+b)
3
=a
3
+b
3
+3ab(a+b)
=(3)
3
+(2
2
)
3
+3(3)(2
2
)(3+2
2
)+3(3+2
2
)
=27+16
2
+54
2
+72+9+6
2
=108+76
2
Hence,
1/4(x
3
−1/x
3
)=1/4(108+76
2
)
=27+19
2
Answered by
3
Answer:
Step-by-step explanation:
(x−1x)3=(x3−1x3)−3⋅x⋅1x⋅(x−1x)
x3−1x3=(x−1x)3+3(x−1x)
x3−1x3=(3+22–√)3+3(3+22–√)
=3+22–√((3+22–√)2+3)
=(3+22–√)(9+8+122–√+3)
=(63+362–√+422–√+24⋅2
=63+48+78–√2
=111+78–√2
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