Question

if a-b+c=8 and ca-ab-bc=18 find a^2+b^2+c^2

Answer 1

Answer:

a² + b² + c² = 28

Step-by-step explanation:

We know that,

${(a - b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ac - ab - bc)$

$a - b + c = 8$

$ca - bc - ab = 18$

Let us substitute the given information in the formula,

${8}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(18)$

${a}^{2} + {b}^{2} + {c}^{2} = 64 - 36$

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