without actually calculating of the cubes,find the value of 14 cube + 13 cube- 27 cube x+1/x
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Step-by-step explanation:
Use the formula:
a³ + b³ = (a+b)(a²-ab+b²)
a³ - b³ = (a-b)(a²+ab+b²)
14³ + 13³ - 27³
= (14+13)(196 - 182 + 169) - 27³
= 27(183) - 27³
= 4941 - 27³
= 28 + 4913 - 27³
= 28 + 17³ - 27³
= 28 + (17 - 27)(289 + 459 + 729)
= 28 - 10(1477)
= - 14742
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