If a + b + c = 5 , ab + bc + ca = 10 , then prove that a^3 + b^3 + c^3 = -25
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a³+b³+c³-3abc= -25
Step-by-step explanation:
from question , we know that ,
a+b+c = 5
ab + bc + ac = 10
a³+b³+c³-3abc = (a+b+c) ( a²+b²+c²-ab-bc-ac)
=5[ (a+b+c)²-3ab-3bc-3ac]
=5[(5)²-3(ab+bc+ac)]
=5(25-30)
=5(-5)
= -25
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