2 years ago

If (a+b+c) = 5 and ab+bc+ac = 10. Prove that a3+b3+c3 -3abc = -25

Mathematics

1 answer:

maks197457 [2]2 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

Using the identity

(a + b + c)³ = a³ + b³ + c³ + 3 [ (a + b + c)(ab + bc + ac) - abc ], then

5³ = a³ + b³ + c³ + 3(5 × 10) - 3abc, that is

125 = a³ + b³ + c³ + 150 - 3abc, hence

a³ + b³ + c³ - 3abc = 125 - 150 = - 25

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If (a+b+c) = 5 and ab+bc+ac = 10. Prove that a3+b3+c3 -3abc = -25​

If (a+b+c) = 5 and ab+bc+ac = 10. Prove that a3+b3+c3 -3abc = -25