Question

If a+b+c=9 and a2+b2+c2= 35 , find the value of (a3+ 3+c3=3abc​

Answer 1

Step-by-step explanation:

Given,

a + b + c = 9 ...(i)

a² + b² + c² = 35 ...(ii)

➽ (a + b + c)² - 2 (ab + bc + ca) = 35

➽ 9² - 2 (ab + bc + ca) = 35

➽ 2 (ab + bc + ca) = 81 - 35

➽ 2 (ab + bc + ca) = 46

➽ ab + bc + ca = 23 ...(iii)

Now,

a³ + b³ + c³ - 3abc

= (a + b + c) (a² + b² + c² - ab - bc - ca)

= (a + b + c) {(a² + b² + c²) - (ab + bc + ca)}

= 9 (35 - 23), using (i), (ii) and (iii)

= 9 × 12

= 108

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