Question

Determinați mulțimea soluțiilor fiecărei ecuaţii: a) x² = 9; b) 3x² = 12; f) (2x + 1)² = 49; e) (2x - 3)² = 25; 36 c) 2x² - 72 = 0; g) (2x + 5)² = 81; d) (x - 2)² = 25; h) (2x - 5)² = 121.​

Answer 1

Răspuns:

Explicație pas cu pas:

a) x² = 9 => x₁,₂ = ±3

b) 3x² = 12 <=> x² = 4 =>  x₁,₂ = ±2

c) 2x² - 72 = 0 <=> 2x² = 72 <=> x² = 36 =>

x₁,₂ = ±6

d) (x - 2)² = 25 <=> Ix-2I = 5 =>

x-2 = 5 => x₁ = 7 ; -x+2 = 5 => x₂ = -3

e) (2x - 3)² = 25 => I2x-3I = 5 =>

2x-3 = 5 => 2x = 8 => x₁ = 4

-2x+3 = 5 => 2x = -2 => x₂ = -1

f) (2x + 1)² = 49 => I2x+1I = 7 =>

2x+1 = 7 => 2x = 6 => x₁ = 3

-2x-1 = 7 => 2x = -8 => x₂ = -4

g) (2x + 5)² = 81 => I2x+5I = 9 =>

2x+5 = 9 => 2x = 4 => x₁ = 2

-2x-5 = 9 => 2x = -14 => x₂ = -7

h) (2x - 5)² = 121 => I2x-5I = 11 =>

2x-5 = 11 => 2x = 16 => x₁ = 8

-2x+5 = 11 => 2x = -6 => x₂ = -3