If (x² + 1/x²) = 38 then find
1. x - 1/x
2. x⁴ + 1/x⁴
Answers
Answered by
0
Answer:
x−
x
1
We have,
(x−
x
1
)
2
=x
2
−2×x×
x
1
+
x
2
1
⇒(x−
x
1
)
2
=x
2
−2+
x
2
1
⇒(x−
x
1
)
2
=x
2
+
x
2
1
−2
⇒(x−
x
1
)
2
=27−2[∵x
2
+
x
2
1
=27 given]
⇒(x−
x
1
)
2
=25⇒(x−
x
1
)
2
⇒x−
x
1
=±5
[Taking square root of both sides]
Answered by
4
Required Answer:-
Given:
- x² + 1/x² = 38.
To Find:
- x - 1/x = ?
- x⁴ + 1/x⁴ = ?
Formulae To Be Used:
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
Solution:
Given that,
➡ x² + 1/x² = 38
Subtracting 2 from both sides, we get,
➡ x² + 1/x² - 2 = 38 - 2
➡ (x)² + (1/x)² - 2 × (x) × (1/x) = 36
Now, this is in (a - b)² form. So,
➡ (x - 1/x)² = 36
➡ x - 1/x = ±√36
➡ x - 1/x = ±6
★ Hence, x - 1/x = ±6
Again,
➡ x² + 1/x² = 38
Squaring both sides, we get,
➡ (x²)² + (1/x²)² + 2 × (x²) × (1/x²) = 1444
➡ x⁴ + 1/x⁴ + 2 = 1444
➡ x⁴ + 1/x⁴ = 1442
★ Hence, x⁴ + 1/x⁴ = 1442
Answer:
- x - 1/x = ±6
- x⁴ + 1/x⁴ = 1442.
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