Question

If
${a}^{2} + b^{2} + c ^{2} = ab + bc + ca$
find the value of
$(a + c) \div b$
​

Answer 1

a+b+c=12

(a+b+c)2=122

a2+b2+c2+2(ab+bc+ca)=144

64+2(ab+bc+ca)=144

ab+bc+ca=144−642

=40

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Answer 2

Answer:

Using the identity is (a+b+c)

2

=a

2

+b

2

+c

2

+2ab+2bc+2ca

It is given that a

2

+b

2

+c

2

=50 and ab+bc+ca=47, therefore,

(a+b+c)

2

=a

2

+b

2

+c

2

+2ab+2bc+2ca

=a

2

+b

2

+c

2

+2(ab+bc+ca)

=50+(2×47)

=50+94=144

⇒(a+b+c)

2

=144

⇒a+b+c=−

144

,

144

⇒a+b+c=−12,12

Hence, the value of (a+b+c) is −12 or 12.