Is x^4 + 1/x^4 = (x + 1/x)^4?
Answers
Answered by
1
Step-by-step explanation:
ANSWER
x
4
+
x
4
1
=119
Adding 2 on both the sides,
x
4
+
x
4
1
+2=119+2
(x
2
+
x
2
1
)
2
=121⇒x
2
+
x
2
1
=11
Subtracting 2 on both sides.
x
2
+
x
2
1
−2=11−2
(x−
x
1
)
2
=9⇒x−
x
1
=±3
Hence, x−
x
1
=3.
Answered by
4
Hi ,
It is given that ,
x + 1/x = 4 ---( 1 )
Do the square of equation ( 1 ),
( x + 1/x )² = 4²
x² + 1/x² + 2 = 16
x² + 1/x² = 16 - 2
x² + 1/x² = 14 --( 2 )
Again do the square of equation ( 2 ),
( x² + 1/x² )² = 14²
x⁴ + 1/x⁴ + 2 = 196
x⁴ + 1/x⁴ = 196 - 2
= 194
I hope this helps you.
:)
Or
⟹ x^4+1/x^4
⟹ (x^2+1/x^2) = (x^4+1/x^4) + 2
⟹ (x^4+1/x^4) = (x^2 + 1/x^2) -2
⟹ (x^4+1/x^4) = (14)^2 - 2
⟹ (x^4+1/x^4) = 196 - 2
⟹ (x^4+1/x^4) = 194
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