Question

A+b+c=m,a2+b2+c2=n,a3+b3=p3. If c=0 then prove that m3+2p3=3mn

Answer 1

Answer:

a + b + c = m

=> (a + b+ c)³= m³

⇔m³ = a³ + b³ +c³ + 3(a + b)(a + c)(c + b)

=> m³ + 2p³ = 3a³ + 3b³ + c³ + 3(a + b)(a + c)(b + c)

with c = 0 => m³ + 2p³ = 3a³ + 3b³ + 3ab(a + b)

have:

3mn = 3(a + b + c)(a² + b² + c²)

with c = 0

=> 3mn = 3(a + b)(a² + b²) = 3[a³ + ab² + ba² + b³]

=  3a³ + 3b³ + 3(a²b + ab²)

= 3a³ + 3b³ + 3ab(a + b)

= m³ + 2p³

=> 3mn = m³ + 2p³

Step-by-step explanation:

Answer 2

Answer:

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