Use the way that kids use i.e trial and error method .
Solution:-
The set given by
[tex]\\ \rm\longmapsto \left\{32+n,\dfrac{n}{8},\sqrt{n+225}\right\}[/tex]
Lets understand
- See the first term any natural value will make it natural .
Come to 2nd one.
- n should be a multiple of 8 to make it whole.
Come to third one
- n should be a number which makes the sum a perfect square by which we get a natural no.We have to solve it w.r.t to 2nd one
Lets think
Nearest squares to 225 are 196 and 289
We can't take 196 as we have to take a positive one other wise it will come in terms of i.
Take 289
[tex]\\ \rm\longmapsto n+225=289[/tex]
[tex]\\ \rm\longmapsto n=289-225=64[/tex]
Its divisible by 8 .
Rewrite the set
[tex]\\ \rm\longmapsto \left\{64+32,\dfrac{64}{8},\sqrt{225+64}\right\}[/tex]
[tex]\\ \rm\longmapsto \left\{96,8,\sqrt{289}\right\}[/tex]
[tex]\\ \rm\longmapsto \left\{96,8,17\right\}[/tex]
Hence n=64
