Question

iii) If a + b + c = 9 and 2(ab + bc + ca) = 24 , find a ^ 2 + b ^ 2 + c ^ 2

Answer 1

➡️ a + b + c = 9

( squaring on both sides )

$( {a + \: b + \: c \: })^{2} = {9}^{2}$

${a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) = 81$

${a}^{2} + {b}^{2} + {c}^{2} + 24 = 81$

${a}^{2} + {b}^{2} + {c}^{2} = 81 - 24$

${a}^{2} + {b}^{2} + {c}^{2} = 57$

Hope it helps ❗

Answer 2

Answer:

57

Step-by-step explanation:

$a {}^{2} + b {}^{2} + c {}^{2} \\ = (a + b + c) {}^{2} - 2(ab + bc + ca) \\ = (9) {}^{2} - 24 \\ = 81 - 24 \\ = 57$