Question

Expand (a/bc+b/ca+c/ab)^2

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept:

Algebraic Identities:

1) (x + y)²  = x² + y² + 2xy

2) (x - y)²  = x²  + y²  - 2xy

3) ( x + y + z)²  = x²  + y²  + z²  + 2xy + 2yz + 2zx

4) ( x - y - z)²  = x²  + y²  + z²  - 2xy + 2yz - 2zx

Given:

(a/bc + b/ca + c/ab)²

Find:

Expand (a/bc + b/ca + c/ab)²

Solution:

= (a/bc + b/ca + c/ab)²

Using the third identity, we get

= (a/bc)²  + (b/ca)²  + (c/ab)²  + 2(a/bc)(b/ca) + 2(b/ca)(c/ab) + 2(c/ab)(a/bc)

= (a²/b²c²) + (b²/c²a²) + (c²/a²b²) + 2/c² + 2/a² + 2/b²

$= \frac{a^4 + b^4 + c^4 + 2a^2b^2 + 2b^2c^2 + 2a^2c^2}{a^2b^2c^2} \\\\= \frac{(a^2 + b^2 + c^2)^2}{a^2b^2c^2}$

Hence, (a/bc + b/ca + c/ab)²  = $\frac{(a^2 + b^2 + c^2)^2}{a^2b^2c^2}$.

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