Question

If (x + ¹/x) = 5, find the value of l) (x² + 1/x²) ll) (x⁴ + 1/x⁴)​

Answer 1

EXPLANATION.

⇒ (x + 1/x) = 5.

As we know that,

Squaring on both sides of the equation, we get.

⇒ (x + 1/x)² = (5)².

⇒ x² + (1/x)² + 2(x)(1/x) = 25.

⇒ x² + 1/x² + 2 = 25.

⇒ x² + 1/x² = 25 - 2.

⇒ x² + 1/x² = 23.

Again, squaring on both sides of the equation, we get.

⇒ (x² + 1/x²)² = (23)².

⇒ (x²)² + (1/x²)² + 2(x²)(1/x²) = (23)².

⇒ x⁴ + 1/x⁴ + 2 = 529.

⇒ x⁴ + 1/x⁴ = 529 - 2.

⇒ x⁴ + 1/x⁴ = 527.

Answer 2

$\huge\colorbox{lavender}{Answer}$

x+1/x = 5

(x+1/x)2 = x2+1/x2 + 2

(5)2 = x2 + 1/x2 + 2

25-2 = x2 +1/x2 = 23

(x2+1/x2) 2= x4 +1/x4+2

(23)2 = x4 +1/x4+2

529-2= x4 +1/x4

527 = x4+1/x4

$\huge\colorbox{pink}{hope it helps u}$

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