Question

if x + 1/x=5 , find the value of x^4 + 1/x^4​

Answer 1

Answer:

x+1=5x

5x-x=1

4x=1

x=1/4

now,

=(1/4)^4+(1/4)^4

=(1/256)+(1/256)

=(2/256)

=128

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Answer 2

Given :-

• x + 1/x = 5

To find :-

• x⁴ + 1/x⁴

Solution :-

→ x + 1/x = 5

• Squaring both side

→ (x + 1/x)² = (5)²

• Apply identity
• (a + b)² = a² + b² + 2ab

→ x² + 1/x² + 2 × x × 1/x = 25

→ x² + 1/x² + 2 = 25

→ x² + 1/x² = 25 - 2

→ x² + 1/x² = 23

• Again squaring both side

→ (x² + 1/x²)² = (23)²

• Apply identity
• (a + b)² = a² + b² + 2ab

→ (x²)² + (1/x)² + 2 × x² × 1/x² = 529

→ x⁴ + 1/x⁴ + 2 = 529

→ x⁴ + 1/x⁴ = 529 - 2

→ x⁴ + 1/x⁴ = 527

Hence,

• The value of x⁴ + 1/x⁴ is 527