Question

If a^2+b^2+c^2=105 ab+bc+ca=92, find the value of a+b+c?

Answer 1

Answer:

17

Step-by-step explanation:

a²+b²+c²=105

ab+bc+ca=92

we know that (a + b + c)² = a² + b² + c² + 2 (ab + bc + ca)

Hence take a square of a + b + c.

(a + b + c)² = 105 + 2 * 92  = 289

a + b + c = √289 = 17.

Answer 2

Step-by-step explanation:

given

${a}^{2} + {b}^{2} + {c}^{2} = 105 \\ ab + bc + ca = 92 \\ now \: according \: to \: formula \\ (a + b + c) {}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + \\ 2(ab + bc + ca) \\ (a + b + c) {}^{2} = 105 + 2 \times 92 \\( a + b + c) {}^{2} = 289 \\ a + b + c = \sqrt{287} = 17$