Question

find the no.s if tehre square sum is 25 times of there sum   and also 50 times there difference

Answer 1

let the numbers be a,b.
a*a + b*b = 25 (a+b) = 50(a - b)
25 (a+b) = 50(a - b)
a+b = (a-b)2
a + b = 2a -2b
a = 3b
b*b + 9 b*b = 100 b
10b*b =100 b
b =10
so a =30 and b=10

Answer 2

let the numbers be a,b
⇒a²+b²=25[a+b]=50[a-b]..........................[1]
we know
[a+b]²=a²+b²+2ab
substitute[1]
⇒[a²+b²]/25=a²+b²+2ab
⇒24[a²+b²]/25=2ab
⇒12a²+12b²-25ab=0
⇒[4a-3b][3a-4b]=0
⇒a=3b/4 and b=3a/4
substitute
a=3b/4 in [1]
⇒[3b/4]²+b²=25[3b/4+b]
⇒25b²/16=25[7b/4]
⇒b=28
substitute b=28 in a=3b/4
⇒a=3[28]/4
⇒a=21
therefore a=21 and b=28