Question

7. Найдите значение выражения а² + b²+c² при аb + ас +bc=11 a+b+c = 6 A) 11 B) 14 C) 15 D) 17 ‍♂️​

Answer 1

$\displaystyle\bf\\a+b+c=6\\\\\Big[(a+b)+c\Big]^{2} =6^{2} \\\\a^{2} +2ab+b^{2} +2\cdot(a+b)\cdot c+c^{2} =36\\\\a^{2} +2ab+b^{2} +2ac+2bc+c^{2} =36\\\\\\(a^{2} + b^{2} + c^{2} )+2\cdot(\underbrace{ab+ac+bc}_{11})=36\\\\(a^{2} + b^{2} + c^{2} )+22=36\\\\a^{2} + b^{2} + c^{2} =36-22\\\\a^{2} + b^{2} + c^{2} =14$