Question

IF A^2+B^2+C^2=74 and ab+bc+ac=61,find a+b+c

Answer 1

Answer:

14

Step-by-step explanation:

We will use the identity :

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

( we will put the values given to us. )

( a+b+c ) ^2 = 74 + 2( 61 )

( a+b+c ) ^2= 74 + 122

( a+b+c )^2 = 196.

a+b+c = √196

( square root of 196 is 14 )

a+b+c = 14

Answer 2

A^2+B^2+C^2=74

AB+BC+CA=64. ,(A+B+C)^2=A^2+B^2+C^2+2(AB+BC+CA)=(A+B+C)^2=74+2(61)=74+122=196=A+B+C=14.