Q. 374.1( 12 Votes )

Without actually

Answer :

(i)


Let a =1/2, b=1/3and c= −5/6




=0/6


= 0


(1/2)3 + (1/3)3 + (5/6)3


= 3 (1/2) (1/3) (−5/6)


= −5/12


[a3 + b3 + c3–3abc =(a + b + c)(a2 + b2 + c2 ab bc−ca)]


[ if 𝑎 + 𝑏 + 𝑐 = 0, 𝑎3 + 𝑏3 + 𝑐3 = 3𝑎𝑏𝑐]


(ii) . Given that: (0.2)3 − (0.3) 3 + (0.1)3


Let a = 0.2, b= −0.3 and c= 0.1


a + b + c = 0.2 − 0.3 + 0.1 = 0.3 − 0.3 = 0


(0.2)3 + (−0.3)3 + (0.1)3


= 3(0.2)(−0.3)(0.1)


= −0.018


[ a3 + b3 + c3 – 3abc= (a + b + c)(a2 + b2 + c2 ab bc ca)]


[if a + b + c = 0, a3 + b3 + c3= 3abc]


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