Question

Determine the value of a^2 +b^2+c^2, if a+b+c=7 and ab+bc+ca=15
​

Answer 1

19

Step-by-step explanation:

`(a + b + c)^(2) \\= a^2 +b^2+c^2 + 2ab + 2bc + 2ca \\ \\ (a + b + c)^(2) \\ = a^2 +b^2+c^2 + 2(ab + bc + ca) \\ \\ (7) ^(2) = a^2 +b^2+c^2 + 2(15) \\ \\ 49 = a^2 +b^2+c^2 + 30 \\ \\ a^2 +b^2+c^2 = 49 - 30 \\ \\ \huge \red{a^2 +b^2+c^2} \blue{= } \purple{19} \\ \\`