Question

Find the product by suitable identity (x + 1/x) (x - 1/x) (x 2 + 1/x 2 ) (x 2 + 1/x 2 )

Answer 1

(x + 1/x)(x - 1/x) + (x² + 1/x²)(x² + 1/x²)

we will use,

(a + b)(a - b) = (a² - b²) in the first expression , and

(a + b)² = a² + 2ab + b² in the second expression

so,

(x + 1/x)(x - 1/x) + (x² + 1/x²)(x² + 1/x²)

= (x² - 1/x²) + (x^4 + 2 + (1/x^4))

after simplicification, we get

x^4 + x² + (1/x^4) - (1/x²) + 2