Question

If a + b + C = 12 and a2 + b2 + c2 =54, find the value of ab + bc

Answer 1

Answer:

ab + bc + ca = 45

Step-by-step explanation:

$a + b + c = 12 \: \\ {a}^{2} + {b}^{2} + {c}^{2} = 54 \\ ab + bc + ca \: = \: ? \: \\ = > {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) \\ = {(12)}^{2} = 54 + 2(ab + bc + ca) \\ = > 144 = 54 + 2(ab + bc + ca) \\ = > 144 - 54 = 2(ab + bc + ca) \\ = > 90 = 2(ab + bc + ca) \\ = > \frac{90}{2} = ab + bc + ca \\ = > ab + bc + ca = 45$

Answer 2

Given →

• a + b + c = 12

• a² + b² + c² = 54

To Find →

The value of ab + bc + ca

ab + bc + ca = ?

$\rule{200}{1}$

Step by step Explanation →

a + b + c = 12

Squaring of both sides →

(a + b + c)² = (12)²

Using the identity →

• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

a² + b² + c² + 2(ab + bc + ca) = 144

But a² + b² + c² = 54 (Given)

=> 54 + 2(ab + bc + ca) = 144

2(ab + bc + ca) = 144 - 54

2(ab + bc + ca) = 90

ab + bc + ca = 90/2

$\boxed{ab + bc+ ca = 45}$

$\rule{200}{1}$

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