Answer :

To find [tex]\( ab + bc + ca \)[/tex] given [tex]\( a + b + c = 13 \)[/tex] and [tex]\( a^2 + b^2 + c^2 = 69 \)[/tex], we can use the following identity:

[tex]\[ (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca). \][/tex]

First, we substitute the given values into this identity:
[tex]\[ (13)^2 = 69 + 2(ab + bc + ca). \][/tex]

Next, we calculate [tex]\( (13)^2 \)[/tex]:
[tex]\[ 169 = 69 + 2(ab + bc + ca). \][/tex]

Now, isolate [tex]\( 2(ab + bc + ca) \)[/tex] by subtracting 69 from both sides:
[tex]\[ 169 - 69 = 2(ab + bc + ca), \][/tex]
[tex]\[ 100 = 2(ab + bc + ca). \][/tex]

To solve for [tex]\( ab + bc + ca \)[/tex], we divide both sides of the equation by 2:
[tex]\[ ab + bc + ca = \frac{100}{2}, \][/tex]
[tex]\[ ab + bc + ca = 50. \][/tex]

Thus, the value of [tex]\( ab + bc + ca \)[/tex] is 50.

The correct answer is:
b) 50

Thanks for taking the time to read If tex a b c 13 tex and tex a 2 b 2 c 2 69 tex then find tex ab bc ca tex A. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada