Question

If a2+b2+c2=83 and ab+bc+CA=71, then the value of a+b+c=

Answer 1

Answer:

Given a²+b²+c²=83

And ab+bc+ca=71

or 2ab+2bc+2ca=142

Now (a+b+c)²=a²+b²+c²+2ab+2bc+2ca

or (a+b+c)²=83+142=225

or a+b+c=±15

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Answer 2

$\huge\underline\mathbb{\red S\pink{O}\purple{L} \blue{UT} \orange{I}\green{ON :}}$

★ Given that,

• a² + b² + c² = 83
• ab + bc + ac = 71

★ To find,

• a + b + c = ?

By using the identity,

$\tt\:(a + b + c)² = a² + b² + c² + 2(ab + bc + ac)$

• Substitute the values.

$\tt\:⟹(a + b + c)² = 83 + 2(71)$

$\tt\:⟹(a + b + c)² = 83 + 142$

$\tt\:⟹(a + b + c)² = 225$

$\tt\:⟹(a + b + c) = \sqrt{225}$

$\tt\:⟹(a + b + c) = 15$

$\underline{\boxed{\bf{\purple{∴ The\:value\:of\:(a + b +c) \:=\:15 \: .}}}}$