Question

if show that (x power a+b) power2 (x power b+c) power2 (x power c+a) power2 / (x power a x power b x power c) power 4 =1​

Answer 1

To prove :

$\frac{{ ({x}^{(a + b)} )}^{2} \times ( { {x}^{(b + c)}) }^{2} \times {( {x}^{(c + a)}) }^{2} }{ {( { x}^{a} \times {x}^{b} \times {x}^{c}) }^{4} } =1$

Proof :

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

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

$= \frac{ {x}^{2a + 2b} \times {x}^{2b + 2c} \times {x}^{2c + 2a} }{ {x}^{4a + 4b + 4c} }$

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

$= \frac{ {x}^{4a + 4b + 4c} }{ {x}^{4a + 4b + 4c} }$

$= 1$

LHS = RHS

hence proved