a + b = 18 .......................................................(1)
a^2 + b ^2 = 290 ...............................................(2)
we will use the algebraic identity formula
(a + b) ^2 = a ^2 + b^2 + 2ab.............................(3)
18^2 = 290 = 2ab
324 - 290 = 2ab
34 = 2ab
ab = 34 /2
ab = 17,..............................................................(4)
a = 17 / b............................................................ (5 )
apply (5) in (1) we get,
a + b = 18
17/ b + b = 18
17+ b^2 = 18b
b^2 - 18b + 17
(b - 17) (b -1)
b = 17,1 ..............................................................(6)
if b= 17 apply in 5 we get
a = 17/17
a = 1
if b= 1
then a = 17,
(a,b) = ( 17,1) or ( a,b) = (1,17)
