Question

Sabendo que x.y = 12 e que x+y = 48 , Determine O valor da expressao x-¹ +y-¹

Answer 1

Sabendo que x.y = 12 e que x+y = 48 , Determine O valor da expressao x-¹ +y-¹

{x.y=12
{x+y=48-->x= 48-y

x.y=12
(48-y).y=12
48y-y^2=12
-y^2+48y=12
-y^2+48y-12=0*(-1)
y^2-48y+12=0---->a=1;b=(-48);c=12
/\=b^2-4ac
/\=(-48)^2-4.1.12
/\=2304-48
/\=2256
/\=4\/141

x= - b+ - \/d/2a

{x'= - (-48)+ 4\/141/2.1
{x'= 24 + 2\/141
:
{x"= -(-48) - 4\/141/2.1
{x"= 24 - 2\/141/2

solução :

(x1,y2)=( 24 - 2\/141 ; 24 + 2\/141 )
(x2,y2)=( 24 + 2\/141 ; 24 -2\/141 )

agora vamos achar : Determine O valor da expressao x-¹ +y-¹

(24 - 2\/141)-¹ + (24 + 2\/141)-¹=>

1/24. -2\/141 + 1/24+2\/141=>

24+2\/141/12 + 24-2\/141/2=>

12+6\/141/6 + 12-6\/141/6=>

12+6\/141+12-6\/141/ 6=>

24/6 =>

4


resposta : 4