Answer:
n = 59
Step-by-step explanation:
The given equation of n is [tex]\sqrt{n + 5} - \sqrt{n - 10} = 1[/tex] and we have to solve it for n.
[tex]\sqrt{n + 5} - \sqrt{n - 10} = 1[/tex] ........... (1)
⇒ [tex]\frac{(n + 5) - (n - 10)}{\sqrt{n + 5} + \sqrt{n - 10}} = 1[/tex]
{Rationalizing the numerator}
⇒ [tex]\sqrt{n + 5} + \sqrt{n - 10} = 15[/tex] .............. (2)
Now, adding (1) and (2) we get
[tex]2\sqrt{n + 5} = 16[/tex]
⇒ n + 5 = 64 {Squaring both sides}
⇒ n = 59 (Answer)
