If x⁴ + 1\x⁴ = 2 find x + 1\x of Maths.
Answers
Answered by
0
Answer:
x4+1x4=47
⟹x4+1x4+2=49
⟹(x2+1x2)2=49
⟹x2+1x2=±7
⟹x2+1x2+2=2±7
⟹(x+1x)2=2±7
⟹x+1x=±2±7−−−−√={3,−3,i5–√,−i5–√}
Answered by
4
Required Answer:-
Given:
To find:
Solution:
This question can be solved by using the identity (a + b)² = a² + b² + 2ab. Let's solve.
We have,
Adding 2 to both sides, we get,
This is in the form of (a + b)². So,
We omit the negative value because x² must be positive if it is a real number. So x² + 1/x² must be positive.
Therefore,
Now, adding 2 to both sides, we get,
Again, it is in (a + b)² form. So,
★ Hence, the value of x + 1/x is 2.
Answer:
- The value of x + 1/x is ±2
Identity Used:
- (a + b)² = a² + 2ab + b²
More Identities:
- (a - b)² = a² - 2ab + b²
- a² - b² = (a + b)(a - b)
- (a + b)² = (a - b)² + 4ab
- (a - b)² = (a + b)² - 4ab
- (a + b)³ = a³ + 3a²b + 3ab² + b³
- (a - b)³ = a³ - 3a²b + 3ab² + b³
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