square root n+5-square root n-10=1
[tex]\sqrt{n+5} - \sqrt{n-10} =1[/tex]
add sqrt(n-10) on both sides
[tex]\sqrt{n+5} =1+ \sqrt{n-10}[/tex]
To remove square root we take square on both sides
[tex](\sqrt{n+5})^2 =(1+ \sqrt{n-10})^2[/tex]
[tex]n+5=(1+ 2\sqrt{n-10} +n -10)[/tex]
[tex]n+5=2\sqrt{n-10} +n -9[/tex]
Subtract n and add 9 on both sides
[tex] 14=2\sqrt{n-10}[/tex]
Now we divide both sides by 2
[tex]7=\sqrt{n-10}[/tex]
Take square on both sides
+-49= n - 10
49 = n-10 and -49 = n - 10
Add 10 on both sides
n= 59 and n = -39
Now we verify both solutions
When n = -39 we will get negative under the square root . that is complex so we ignore n=-39
n = 59 is our solution
Answer:
the value of n is 59
Step-by-step explanation:
plato says it was right (:
