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2x² - 3² = (x-3)²-(x+3)²
2x² - 9 = x² - 6x + 9 - (x² + 6x + 9)
2x² - 9 = x² - 6x + 9 - x² - 6x - 9
2x² - 9 = -12x
2x² + 12x - 9 = 0
Δ = 12² - 4 × 2 × (-9) = 144 + 72 = 216
√Δ = √216 = 9√6
x₁ = (-b + Δ) : 2a = (-12 + 9√6) : 4 = -3 + 9√6/4
x₂ = (-b - Δ) : 2a = (-12 - 9√6) : 4 = -3 - 9√6/4
Odp: Liczba ta to -3 + 9√6/4 albo -3 - 9√6/4.
Ad 2.
[x+1/2]² ze wzoru skróconego mnożenia (a+b)² = a²+2ab-b²
[x-1][x+1] ze wzoru skróconego mnożenia (a-b)(a+b) = a²-b²
[x+1/2]²-[x-1][x+1] = 16
x² + x + 1/4 - (x² - 1) = 16
x² +x + 1/4 - x² +1 = 16
x + 5/4 = 16
x = 14 3/4