Question
 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]Solution
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.
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