Question

If (a + b + c) =14 and (a sq + b sq + c sq) =74, find the value of (ab + bc + ca).​

Answer 1

Step-by-step explanation:

$(a + b + c) = 14$

${(a + b + c)}^{2} = {14}^{2}$

${(a + b + c)}^{2} = 196$

${a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ac = 196$

$({a}^{2} + {b}^{2} + {c}^{2}) + 2ab + 2bc + 2ac = 196$

$74 + 2ab + 2bc + 2ac = 196$

$2(ab + bc + ac) = 196 - 74$

$2(ab + bc + ac) = 122$

$ab + bc + ac = \frac{122}{2}$

$ab + bc + ac = 61$

Answer 2

Answer:

61

Step-by-step explanation:

(a + b + c) =14 and (a sq + b sq + c sq) =74, find the value of (ab + bc + ca).

than,(a+b+c)^2=14^2

(a+b+c)^2=a^2+b^2+c^2+[2(ab+bc+ca)]=14×14=196

74+2(ab+bc+ca)=196

ab+bc+ca=(196-74)/2=61

ab+bc+ca=61

Thank you ☺☺