Question

$calcuati \: |x + y| - |x - y| \: stiind \: ca \: {x}^{2} + {y}^{2} = 52 \: si \: x \times y = 24 \:$
va rog :3​

Answer 1

Răspuns:

Explicație pas cu pas:

x^2 + y^2 = 52

x*y = 24

x^2 + y^2 + 2x*y = 52 + 2*24 = 52 + 48 = 100

(x + y)^2 = 100

Ix + yI = 10

x^2 + y^2 - 2x*y = 52 - 2*24 = 52 - 48 = 4

(x - y)^2 = 4

Ix - yI = 2

Ix + yI - Ix - yI = 10 - 2 = 8

Answer 2

Răspuns:

Ix+yI - Ix-yI = 8

Explicație pas cu pas:

x²+y² = 52

x·y = 24

(x+y)² = x²+2xy + y² =>

(x+y)² = (x²+y²) + 2·xy = 52 + 2·24 = 52+48 = 100 =>

x+y = √100 => x+y = 10

x+y = 10 => x = 10-y

xy = 24

(10-y)·y = 24 => 10y-y² = 24 => y²-10y+24 = 0

<=> y²-4y-6y+24 = 0 <=> y(y-4)-6(y-4) = 0 <=>

(y-4)(y-6) = 0 => y₁ = 4 ; y₂ = 6

i) y₁ = 4 => x₁ = 6  ;

ii) y₂ = 6 ; x₂ = 4

i) Ix+yI - Ix-yI = I6+4I -I6-4I = I10I - I2I = 10-2 = 8

ii) Ix+yI - Ix-yI = I4+6I - I4-6I = I10I - I-2I = 10-2 = 8