Question

if a square + b square + c square=35 and ab + bc + ca =23 the value of a +b+c​

Answer 1

Answer:

9

Step-by-step explanation:

(a+b+c)^2= a^2+b^2+c^2+2(ab+bc+ca)

(a+b+c)^2=35+2*23

(a+b+c)^2=35+46 =81

(a+b+c). =9

Answer 2

Given,

${a}^{2} + {b}^{2} + {c}^{2} = 35$

$ab + bc + ac = 23$

Now, we know that,

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

So, putting all the required values, we get,,

${(a + b + c)}^{2} = 35 + (2 \times 23)$

$\implies {(a + b + c)}^{2} = 81$

$\implies a + b + c = \sqrt{81}$

$\implies a + b + c = \pm9$