Question

a+b+c=8and ab+bc+ca=18find the value of a²+b²+c²​

Answer 1

Answer:

100

Step-by-step explanation:

as (a^2+b^2+c^2)=a^2+b^2+c^2+2ab+2vc+2ca

thus answer is 100

Answer 2

Answer:

${a}^{2} + {b}^{2} + {c}^{2} = 28$

Step-by-step explanation:

a+b+c = 8 and ab+bc+ca = 18

Taking first equation

$a + b + c = 8 \\ squaring \: both \: sides \\ {(a + b + c)}^{2} = {8}^{2} \\ {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca = 64$

Second equation

Multiply both sides by 2

2ab +2bc +2ca = 36

${a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca = 64 \\ substitute \: the \: value \: in \: the \: equation \: i.e. \: 2ab + 2bc + 2ca = 36 \\ {a}^{2} + {b}^{2} + {c}^{2} + 36 = 64 \\ {a}^{2} + {b}^{2} + {c}^{2} = 64 - 36 \\ {a}^{2} + {b}^{2} + {c}^{2} = 28$