Question

if a + b + c = 9 and ab + bc + ca = 23 find the value of a^2 + b^2 + c^2 ?​

Answer 1

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

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

9^2= a^2 + b^2 + c^2 + 2(23)

81 =  a^2 + b^2 + c^2 + 46

144–46 = a^2 + b^2 + c^2

35 = a^2 + b^2 + c^2

Hope this helps!

Answer 2

Answer:

35

Step-by-step explanation:

Given : a + b + c = 9 and ab + bc + ca = 23

therefore we have the formula that

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

                    ⇒     ( 9 ) ² =  a² + b² + c² + 2(23)

                     ⇒      81   =    a² + b² + c² + 46

                     ⇒     81 - 46  =  a² + b² + c²

                       ⇒     35 = a² + b² + c²