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Verified answer
( x₁ + x₂ )( x₁ - x₂ ) = x₁² - x₁x₂ + x₁x₂ - x₂²( x₁ + x₂ )( x₁ - x₂ ) = x₁² - x₂²
x₁² + x₂² = ( x₁ + x₂)² - 2 x₁ x₂
x₁² - x₂² = (x₁ + x₂) (x₁ - x₂)
= √(x₁ + x₂)² (x₁ - x₂)²
= √(x₁² + x₂² + 2x₁x₂)(x₁² + x₂² - 2x₁ x₂)
= √(x₁⁴ + x₂⁴ - 2(x₁ x₂)²
= √{(x₁² + x₂²)² - 4(x₁ x₂)²}
= √{(x₁ + x₂)² - 2(x₁ x₂)}² - 4(x₁ x₂)²
= √{(x₁ + x₂)⁴ - 4(x₁+x₂)²(x₁ x₂) + 4(x₁ x₂)² - 4(x₁x₂)²
= √{x₁ + x₂)⁴ - 4(x₁+x₂)²(x₁ x₂)}