Question

VA ROG MUUUUUUUUUUUUUUUUUUUUUULTTTTTTTTTTT! ​

Answer 1

Explicație pas cu pas:

x-y=9 => (x-y)²=81 => x²-2xy+y²=81 => -2xy=81-305 =>

-2xy=-224 => xy=112

xy=112 => 2xy=224

(x+y)²=x²+2xy+y²=305+224=529

=> x+y=23 (x+y poate fi si -23 dar ne spune ca apartin R+ deci sunt pozitive)

x+y=23

x-y=9

=> 2x=32 => x=16 => y=7

x²+y²=290

xy=143=> 2xy=286

(x+y)²=x²+2xy+y²=576 => x+y=24 (x,y€R+)

(x-y)²=x²-2xy+y²=4 => x-y=2 sau x-y=-2

x+y=24

x-y=2

=> 2x=26 => x=13 => y=11

x+y=24

x-y=-2

=> 2x=22=> x=11 => y=13

x²+y²=48

(x+y)²=x²+y²+2xy=60 => 2xy=12

(x-y)²=x²-2xy+y²=48-12=36 => x-y=6 sau x-y=-6

x-y=3

xy=4 => 2xy=8

(x-y)²=x²-2xy+y²=9 => x²+y²=17

(x+y)²=x²+y²+2xy=17+8=25 => x+y=5 (x,y€R+)

x+y=5

x-y=3

=> 2x=8 => x=4=>y=1

a=3x+9

b=4x+12

c=5x+15

Aplicam reciproca teoremei lui Pitagora:

a²+b²=c² =>

(3x+9)²+(4x+12)²=(5x+15)² =>

9x²+54x+81+16x²+96x+144=25x²+150x+225 =>

25x²+150x+225=25x²+150x+225 (A) =>

triunghiul este dreptunghic