a>1
√(2a + 2√(a² - 1)) = √( a - 1 + 2√(a - 1)(a + 1) + a + 1) = √(√(a - 1)² + 2√(a - 1)√(a + 1) + √(a + 1)²) = √(√(a - 1) + √(a + 1))² = √(a - 1) + √(a + 1)
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a>1
√(2a + 2√(a² - 1)) = √( a - 1 + 2√(a - 1)(a + 1) + a + 1) = √(√(a - 1)² + 2√(a - 1)√(a + 1) + √(a + 1)²) = √(√(a - 1) + √(a + 1))² = √(a - 1) + √(a + 1)