Question

a square + b square + c square is equal to 20 and ab + bc + ca
is equal to 8 find value of a + b + c ​

Answer 1

$\huge\mathfrak{Solution:}$

${a}^{2} + {b}^{2} + {c}^{2} = 20 \\ ab + bc + ca = 8 \\ a + b + c = \: ? \\\ {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) \\ {(a + b + c)}^{2} = 20 + 16 = 36 \\ a + b + c = \sqrt{36} = 6$

$\huge\boxed{a+b+c=6}$

Answer 2

Given :-

$a^2 + b^2 + c^2 = 20$

$ab + bc + ac = 8$

To find:-

The value of a + b + c.

Solution:-

To solve this question we have a proper knowledge of identity.

The required identity to solve this problem is :-

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

• put the given value.

→$( a+b+c)^2 = 20 + 2 \times 8$

→$(a+b+c)^2 = 20 +16$

→$(a +b+c)^2 = 36$

→$a+b+c = \pm\sqrt{36}$

→$a+b+c =\pm 6$

hence ,

The value of a + b + c = ± 6.