Question

if a+b+c=14,a²+b²+c²=100,then what is ab +bc+ca​

Answer 1

Step-by-step explanation:

Given

a + b + c = 14

a² + b² + c² = 100

To find

ab + bc + ca = ?

Solution

As we know that

→ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

→ (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

→ (14)² = 100 + 2(ab + bc + ca)

→ 196 - 100 = 2(ab + bc + ca)

→ 2(ab + bc + ca) = 96

→ ab + bc + ca = 96/2

→ ab + bc + ca = 48

Hence,

• ab + bc + ca = 48

Answer 2

Answer:

96

Step-by-step explanation:

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + ab + bc + ca \\ {14}^{2} = 100 + ab + bc + ca \\ ab + bc + ca = 196 - 100 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 96$