Question

given that (a-b)whole square =50and ab=7 find value of a square+b square​

Answer 1

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If a

2

+b

2

+c

2

=50 and ab+bc+ca=47, find all possible values of a+b+c.

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Solution

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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.