Răspuns
Explicație pas cu pas:
3 / (√5 - √2) = 3(√5 + √2) / (√5 - √2)(√5 + √2) = 3(√5 + √2) / (5 - 2) = √5 + √2
6/(√10 + 1) = 6(√10 - 1) / (√10 + 1)(√10 - 1) = 6(√10 - 1) /(10 - 1) = 6(√10 - 1) /9 = 2(√10 - 1) /3
√10 / (2√5 - √10) = √10 (2√5 + √10) / (2√5 - √10)(2√5 + √10) = √10 (2√5 + √10) / (20 - 10) = √10 (2√5 + √10) /10 = (√2*√5 * 2√5 + 10)/10 = (10√2 + 10) / 10 = √2 + 1
(√6 - √3) / (√6 - √3 - √2) = (√6 - √3)(√6 - √3 +√2) / (√6 - √3 - √2)(√6 - √3 +√2) = (√6 - √3)(√6 - √3 +√2) / (7 - 2√6√3) = (√6 - √3)(√6 - √3 +√2) / (7 - 6√2) = (√6 - √3)(√6 - √3 +√2)(7 + 6√2) / (7 - 6√2)(7 + 6√2) = (√6 - √3)(√6 - √3 +√2)(7 + 6√2) /(49 - 72) = (√6 - √3)(√6 - √3 +√2)(7 + 6√2) /23
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a + b = 3√6
ab = 12
(a + b)^2 = a^2 + b^2 + 2ab
a^2 + b^2 = (a + b)^2 -2ab = (3√6)^2 - 24 = 54 - 24 = 30
