InterviewSolution
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InterviewSolution
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Evaluate the following using suitable identities :(i) (99)3(ii) (102)3(iii) (998)3 |
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Answer» (i) (99)3 = (100 – 1)3 As per Identity, (a – b)3 = a3 – b3 – 3ab(a – b) (100 – 1)3 = (100)3 – (1)3 – 3(100)(1)(100- 1) (99)3 = 1000000 – 1 – 300(100 – 1) = 1000000 – 1 – 30000 + 300 = 970299 ∴ (99)3 = 970299 (ii) (102)3 = (100 + 2)3 As per Identity, (a + b)3 = a3 + b3 + 3ab(a + b) (100 + 2)3 = (100)3 + (2)3 + 3( 100)(2)( 100 + 2) = 1000000 + 8 + 600( 100 + 2) = 1000000 + 8 + 60000 + 1200 (100 + 2)3 = 1061208 ∴ (102)3= 1061208 (iii) (998)3 = (1000 – 2)3 As per Identity, (a – b)3 = a3 – b3 – 3ab(a – b) (1000 – 2)3 = (1000)3 – (2)3 – 3( 1000) (2)(1000 – 2) = 1000000000 – 8 – 6000(1000 – 1) = 1000000000 – 8 – 6000000 + 6000 = 994005992 ∴ (998)3 = 994005992 |
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