Question

if x+1/x=5 find the value of x²-1/x²
answer with step by step explaination​

Answer 1

Answer:

If we recognize that SQUARING x gives us x², and SQUARING 1/x gives us 1/x², then we might try SQUARING both sides of our given equation.

That is: (x + 1/x)² = 5²

In other words: (x + 1/x)(x + 1/x) = 25

Use FOIL to expand: x² + 1 + 1 + 1/x² = 25

Simplify: x² + 2 + 1/x² = 25

Subtract 2 from both sides to get: x² + 1/x² = 23