Question

a+b+c =6 andab+bc+ca=11 find a²+ b+²c²

Answer 1

Answer:

do using the property (a+b+c)² and put values

Answer 2

$\huge{\underline{ Question:}}$

$a+b+c =6 \: \: and \: \: ab+bc+ca=11. \: find \: \: \: a²+ b+²c²$

$\red{ \huge{\underline {\underline{ Answer:}}}}$

$We \: \: are \: \: going \: \: to \: \: use \: \: this \: \: identity \: \: to \: \: solve \: \: this \: \: problem :$

$\large \boxed{(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca}$

$\underline{Given : }$

$a + b + c = 6$

$ab + bc + ca = 11$

${a}^{2} + {b}^{2} + {c}^{2} = \: \: ?$

$We'll \: \: substitute \: \: the \: \: given \: \: values \: \: in \: \: this \: \: i dentity \: ;$

${(6)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2 \: (ab + bc + ac)$

(took 2 as common outside)

$36 = {a}^{2} + {b}^{2} + {c}^{2} + 2 \: (11)$

$36 = {a}^{2} + {b}^{2} + {c}^{2} + 22$

$36 - 22 = {a}^{2} + {b}^{2} + {c}^{2}$

$14 = {a}^{2} + {b}^{2} + {c}^{2}$

$\large \boxed{ {a}^{2} + {b}^{2} + {c}^{2} = 14}$

$\\ \\ \\ \\ \purple{Hope \: \: this \: \: helps \: \: you \: !}$