Question

find the value of ab + bc + c=a if a+b+c =a
and a² +b² +
${c}^{2}$
=35​

Answer 1

Step-by-step explanation:

\textbf{Answer :}Answer :

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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