Q1Long answerExercise 1.3
1 1 5−2 6 5−2 6 5−2 6 b= = = × = 2 2 = =5−2 6 a 5+2 6 5 + 2 6 5 − 2 6 5 − (2 6) 25 − 24 Therefore, a2 + b2 = (a + b)2 – 2ab Here, a + b = (5 + 2 6 ) + (5 – 2 6 ) = 10 ab = (5 + 2 6 ) (5 – 2 6 ) = 52 – ( 2 6 )2 = 25 – 24 = 1 Therefore, a2 + b2 = 102 – 2 × 1 = 100 – 2 = 98
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Rational numbers: (ii), (iii) Irrational numbers: (i), (iv)