Question

Simplify: (xp/xq)p+q . (xq/xr)q+r . (xr/xp)r+p

Answer 1

(xp/xq)p+q*

(xq/xr)q+r*

(xr/xp)r+p

=(xp-q)p+q*

(xq-r)q+r*

(xr-p)r+p

=(x)p2-q2*

(x)q2-r2*

(x)r2-p2

=(x)p2-q2+q2-r2+r2-p2

=(x)0

=1

Answer 2

Concept Introduction:-

Making anything simpler makes it easier to accomplish or understand, or it can be the process itself that makes something simpler.

Given Information:-

We have been given that $(xp/xq)p+q . (xq/xr)q+r . (xr/xp)r+p$

To Find:-

We have to find that Simplify: $(xp/xq)p+q . (xq/xr)q+r . (xr/xp)r+p$

Solution:-

According to the problem

$(\frac{xp}{xq}) (p+q) \times (\frac{xq}{xr}) (q+r)\times (\frac{xr}{xp}) (r+p)\\=(p+q)(q+r)(r+p)\\=(pq+pr+q^2+qr)(r+p)\\=pqr+p^2q+pr^2+q^2r+qr^2+p^2q+p^2r+pq^2+pqr\\=2pqr+2p^2q+pr^2+q^2r+qr^2+p^2r+pq^2$

Final Answer:-

The correct answer after simplification is $2pqr+2p^2q+pr^2+q^2r+qr^2+p^2r+pq^2$.

#SPJ2