1. [√(2 + √3) - √(2 - √3)]² = [√(2 + √3)]² - [2√(2 + √3)(2 - √3)] + [√(2 - √3)]² = = 2 + √3 - 2√(4 - 3) + 2 - √3 = 4 - 2√1 = 4 - 2 * 1 = 4 - 2 = 2 2. [√(8 - √15) + √(8 + √15)]² = [√(8 - √15)]² + [2√(8 - √15)(8 + √15)] + [√(8 + √15)]² = 8 - √15 +2√(64 - 15) + 8 + √15 = 16 + 2√49 = 16 + 2 * 7 = 16 + 14 = 30
1. [latex]\ (sqrt{2+ sqrt{3} } -sqrt{2- sqrt{3} })^2= \ \2+ sqrt{3} -2 sqrt{(2+ sqrt{3})({2- sqrt{3})}} +2- sqrt{3} = \ \4-2 sqrt{4-3} =4-2cdot1=2 [/latex] 2. [latex]\( sqrt{8- sqrt{15} } + sqrt{8+ sqrt{15} })^2= \ \8- sqrt{15}+2 sqrt{(8- sqrt{15})(8+ sqrt{15} )} } } +8+ sqrt{15} = \ \16+2 sqrt{64-15} =16+2 sqrt{49} =16+2cdot7=16+14=30 [/latex]
