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Evaluate each of the following using identities:(i) (399)2(ii) (0.98)2(iii) 991×1009(iv) 117×83 |
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Answer» (i) We will use the identity, (a - b)2 = a2 + b2 – 2ab (399)2 = (400 - 1)2 = (400)2 + (1)2 - 2 x 400.1 = 16000 + 1 - 800 = 159201 (ii) We will use the identity, (a - b)2 = a2 + b2 – 2ab (0.98)2 = (1 - 0.02)2 = (1)2 + (0.02)2 - 2 x 0.02 x 1 = 1 + 0.004 - 0.04 = 0.9604 (iii) We will use the identity, (a - b)(a + b)= a2 - b2 991 x 1009 = (1000 - 9)(1000 + 9) = (1000)2 - (9)2 = 1000000 - 81 = 999919 (iv) We will use the identity, (a - b) (a + b)= a2 - b2 117 x 83 = (100 + 17)(100 - 17) = (100)2 + (17)2 = 10000 - 289 = 9711 |
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