If 1/x =√5 , find the value of x² + 1/x² and x⁴ + 1/x⁴
Answers
Given : x + 1/x = √5 [Mistake in the question]
To find : value of x² + 1/x² and x⁴ + 1/x⁴
Solution :
We have x + 1/x = √5 ……..(1)
On squaring eq 1 both sides,
(x + 1/x)² =√5²
By Using Identity : (a + b)² = a² + b² + 2ab
x² + 1/x² + 2 x × 1/x = 5
x² + 1/x² + 2 = 5
x² + 1/x² = 5 - 2
x² + 1/x² = 3 …………..(2)
On squaring eq 2 both sides,
(x² +1/x² )² = 3²
(x²)² + (1/x²)² + 2 x² × 1/x² = 3²
x⁴ + 1/x⁴ + 2 = 9
x⁴ + 1/x⁴ = 9 - 2
x⁴ + 1/x⁴ = 7
Hence the value of the value of x² + 1/x² is 3 & x⁴ + 1/x⁴ is 7.
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Answer:
Step-by-step explanation:
We have x + 1/x = √5 ……..(1)
On squaring eq 1 both sides,
(x + 1/x)² =√5²
By Using Identity : (a + b)² = a² + b² + 2ab
x² + 1/x² + 2 x × 1/x = 5
x² + 1/x² + 2 = 5
x² + 1/x² = 5 - 2
x² + 1/x² = 3 …………..(2)
On squaring eq 2 both sides,
(x² +1/x² )² = 3²
(x²)² + (1/x²)² + 2 x² × 1/x² = 3²
x⁴ + 1/x⁴ + 2 = 9
x⁴ + 1/x⁴ = 9 - 2
x⁴ + 1/x⁴ = 7