Question

If ab + bc + ca=10 and
${a}^{2} + \: {b}^{2} \ + : {c}^{2}$
= 61 , find the value of (a,b,c)
​

Answer 1

Step-by-step explanation:

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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.