Question

If x=10pq/p+q show that x+5p/x-5p + x+5q/x-5q

Answer 1

Given:

x=10pq/p+q  

To find:

If x=10pq/p+q show that x+5p/x-5p + x+5q/x-5q

Solution:

From given, we have,

x = 10pq/p+q  

we need to find x+5p / x-5p + x+5q / x-5q

First, we need to substitute the value of x in given equation,

x+5p / x-5p + x+5q / x-5q

(10pq/p+q)+5p / (10pq/p+q)-5p + (10pq/p+q)+5q / (10pq/p+q)-5q

further solving we get,

$\dfrac{\frac{10pq}{p+q}+5p}{\frac{10pq}{p+q}-5p}+\dfrac{\frac{10pq}{p+q}+5q}{\frac{10pq}{p+q}-5q}\\=\dfrac{p+3q}{q-p}+\dfrac{3p+q}{p-q}\\=\dfrac{-\left(p+3q\right)}{-\left(q-p\right)}+\dfrac{3p+q}{-\left(q-p\right)}\\=\dfrac{-\left(p+3q\right)+3p+q}{-\left(q-p\right)}\\=-\dfrac{-\left(p+3q\right)+3p+q}{q-p}\\=-\dfrac{2p-2q}{q-p}\\=-\dfrac{-2(q-p)}{q-p}\\=-(-2)\\=2$

∴ x+5p/x-5p + x+5q/x-5q = 2