Question

If a+b+c= 12 and ab+bc+ca= 22, find a²+b²+c²​

Answer 1

Answer:

Here is your answer =>

Step-by-step explanation:

a+b+c = 12

squaring both sides

(a+b+c)^2 = 12^2

a^2 + b^2 + c^2 + 2ab + 2bc + 2ca = 144

a^2 + b^2 + b^2 + 2(ab + bc + ca) = 144

{ Put value of ab + bc + ca = 22 }

a^2 + b^2 + c^2 + 2×22 = 144

a^2 + b^2 + c^2 = 144 - 44

a^2 + b^2 + c^2 = 100

Answer 2

Step-by-step explanation:

Given:-

• a+b+c= 12

• ab+bc+ca= 22

To Find:-

a²+b²+c² = ?

Solution:-

We know that,

$(a+b+c)² = a² + b² + c² + 2(ab + bc + ca) \\ => 12² = a² + b² + c² + 2( 22 ) \\ => 144 = a² + b² + c² + 44 \\ => a² + b² + c² = 144 - 44 \\ \sf{ \pink\therefore \: a² + b² + c² = 100}$