Do you know number theory
If for and , find the number of real pairs for which is a perfect square.
The answer is 11.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
We can represent,21x+20y=420 by a line which intersects y axis at (0,21)and x axis at (20,0) and the x and y have their limit between these numbers.We want the values of (x^2 +y^2)^1/2 which is nothing but distance of points of above line from origin.From the limits of x and y, we can conclude that,we will only take points of hypotenuse of triangle formed by x axis, y axis and the above line except end points.but as mentioned we only want integral solution.Now,from above facts the thing for which we are searching is nothing but integral value cevians to the hypotensue (29)whose other two sides are 21 and 20 and as we know perpendicular will be smallest cevian which is equal to 14.48(approx)..so your result came (20-15)+(21-15) will be your answer which is 11.... Sorry for rip english...if you required answer with actual figure....then telegram me (krity kamal)