Simplify the given expression
[1.5 × 1.5 × 1.5 + 2.7 × 2.7 × 2.7 + 4.8 × 4.8 × 4.8 – 3 × 1.5 × 2.7 × 4.8] / [1.5 × 1.5 +2.7 × 2.7 + 4.8 × 4.8 – 1.5 × 2.7 – 2.7 × 4.8 – 4.8 × 1.5]
Let a = 1.5, b = 2.7 and c =4.8. = [a× a × a + b × b × b + c × c × c – 3 × a × b× c] / [a × a + b × b + c × c – a × b – b × c – c × a] =[a3+b3+c3-3abc] / [a2+b2+c2-ab-bc-ca] As we know that - a3+b3+c3-3abc =(a+b+c) a2+b2+c2-ab-bc-ca =[(a+b+c) a2+b2+c2-ab-bc-ca]/ a2+b2+c2-ab-bc-ca The term (a2+b2+c2-ab-bc-ca) cancel out and leave. =(a+b+c) =1.5+2.7+4.8 = 9.
Three series are provided below. You need to determine the values of A, B, and C and subsequently establish a relationship among them.
I: 4, 10...
9134 170 ? 577 1306
...12 11 18 34 89.5 259.5
...47 54 ? 74 87 ...
30 29 91 446 ? 28217
217 267 304 330 348 357
...5 18 44 83 135 200 ...
1. In series II, if ‘x’ is the right term, then find which of the following statement(s) are true.
I. x/124 is a factor 6 and 8.
2187, 1458, 972, ?, 432, 288
12 7 10 25 107 ?
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