Question

if x=root 7 / 5, 5/x=p*root 7, then find the value of the rational number p

Answer 1

very simple put the value of x in the eq. consisting p:
5/x=p*root7
5÷root7/5=p*root7
5 * 5/root7=p*root7
25/root7=p*root7
now taking root7 from rhs to lhs
25/7=p
ans.

Answer 2

The value of $p=\dfrac{25}{7}$

Step-by-step explanation:

We have,

$x=\dfrac{\sqrt{7}}{5}$                                             ......(1)

and

$\dfrac{5}{x}=p\times \sqrt{7}$      ⇒ $x=\dfrac{5}{p\times \sqrt{7} }$            ......(2)

To find, the value of p = ?

Equating equations (1) and (2), we get

$\dfrac{\sqrt{7}}{5} =\dfrac{5}{p\sqrt{7}}$

⇒ $p\sqrt{7}.\sqrt{7}=5\times 5$

⇒ $7p=25$

⇒ $p=\dfrac{25}{7}$

Thus, the value of $p=\dfrac{25}{7}$