Question

a+b+c=9
ab+bc+ca=11
find a3+b3+c3-3abc​

Answer 1

1. use the formula of a3+b3+c3-3abc and use a+b+c=9 as a formula by squaring both side and then put the value of a2+b2+c2 in equation 1

Answer 2

Answer:

Question :-

➠ a + b + c = 9, ab + bc + ca = 11

find the value of a³ + b³ + c³ - 3abc

Answer :-

➔ a + b + c = 9

➻ (a + b + c)² = (9)²

➻ (a + b + c)² = 81

➻ a² + b² + c² + 2(ab + bc + ac) = 81

➻ a² + b² + c² + 2 × 11 = 81

➻ a² + b² + c² + 22 = 81

➻ a² + b² + c² = 81 - 22

➻ a² + b² + c² = 59

➔ a³ + b³ + c³ - 3abc

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

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

➻ 9 × (59 - 11)

➻ 9 × 48

➻ 432

∴ The value of a³ + b³ + c³ - 3abc is 432