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  • If x = (2 + root(5))^1/2 + (2 - root(5))^1/2 and y = (2+ root(5))^1/2 - (2 - root(5))^1/2 then evaluate x^2 + y^2

If x = (2 + root(5))^1/2 + (2 - root(5))^1/2 and y = (2+ root(5))^1/2 - (2 - root(5))^1/2 then evaluate x^2 + y^2

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x = (2 + \sqrt{5})^\frac{1}{2} + (2 - \sqrt{5})^\frac{1}{2} \\ y = (2 + \sqrt{5})^\frac{1}{2} - (2 - \sqrt{5})^\frac{1}{2} \\\\ x^2 = 2 + \sqrt{5} + 2 - \sqrt{5} + 2 (2 + \sqrt{5})(2 - \sqrt{5}) \\ x^2 = 4 + 2 (4 - 5) \\ x^2 = 2 \\ y^2 = 2 + \sqrt{5} + 2 - \sqrt{5} - 2 (2 + \sqrt{5})(2 - \sqrt{5}) \\ y^2 = 4 - 2 (4 - 5) \\ y^2 = 6 \\ x^2 + y^2 =8

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Ravindra Pindel

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