# Find 2 numbers such that the sum is 18 and sum of their squares is 290

2
by saikrishnan

2014-11-20T17:09:33+05:30
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)

17+1=18,17^2+1^2=290 plz pick it as the best
wow dont u think our answers are somelike same
most welcome
ya i think but i had given the easier way to calculate this answer @Bpjindia0720
2014-11-20T17:15:59+05:30
A + b = 18
a^2 + b ^2 = 290
(a + b) ^2 = a ^2 + b^2 + 2ab
18^2 = 290 = 2ab
324 - 290 = 2ab     34 = 2ab
ab = 34 /2 =17

a = 17 / b
when we put 5 in 1
a + b = 18
17/ b + b = 18
17+ b^2 = 18b
b^2 - 18b + 17
(b - 17) (b -1)
b = 17,1
if b= 17 applied in 5 comes 1
a = 17/17
a = 1
b= 1
a = 17,
b=1
same thinking
oh yes might be
u know that when the concept is same mostly the outcome is same
am i right
yep yep