The sum of two numbers is 8 and the sum of their squares is 34 what is the larger number?

Answer 1

EQ1 x+y=8

EQ2 x2+y2=34

EQ1 x=8-y

EQ1 and EQ2 combined gives (8-y)2+y2=34

simplify

64 -16y +y2+y2=34

simplify

2y2-16y+30=0

solve for -16y

(2y-?)(y-!)=0 EQA

EQ3 -2y!-y?=-16y

simplify

EQ3 2!+? =16

EQ4 ?!=30

EQ3 ?=16-2!

Combined EQ3 and EQ4

gives

(16-2!)!=30

simplify

8!-!2=15

Method of exhaustion

8!-!2 when

!=0 -> 0

!=2 ->12

!=3->15

!=3 into EQ3 gives ?=16-2! gives ?=10

substitute into EQA gives (2y-10)(y-3)=0

solving gives y=5 or 3

solving for EQ1 x+y=8 then x=3 or 5

solving for EQ2 x2+y2=34 gives 9+25 for either combination

so the larger number is 5