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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

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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