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The sum of two numbers is 8 and the sum of their squares is 34 what is the larger number?
Wiki User
∙ 14y ago
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
Wiki User
∙ 14y ago
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