Math, asked by atulyav5, 3 months ago

10 pq
P +q
find the value of
x+5p +x+5q/
x-5p +x-5q

Answers

Answered by krishnagangne
0

Answer:

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Answered by leehyeri
0

Step-by-step explanation:

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,

\begin{gathered}\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\end{gathered}

p+q

10pq

−5p

p+q

10pq

+5p

+

p+q

10pq

−5q

p+q

10pq

+5q

=

q−p

p+3q

+

p−q

3p+q

=

−(q−p)

−(p+3q)

+

−(q−p)

3p+q

=

−(q−p)

−(p+3q)+3p+q

=−

q−p

−(p+3q)+3p+q

=−

q−p

2p−2q

=−

q−p

−2(q−p)

=−(−2)

=2

∴ x+5p/x-5p + x+5q/x-5q = 2

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