Rozwiązane

(x√2 - 1) (x√2 + 1) - (x√2 - 1)² + (x - √2)² + 5 ≤ x(x - 2)

Odpowiedź :

Domaskowaviz
(x√2 - 1) (x√2 + 1) - (x√2 - 1)² + (x - √2)² + 5 ≤ x(x - 2)
(x√2)² - 1² - (x√2² - 2x√2 + 1²) + (x² - 2x√2 + √2²) + 5 ≤ x² - 2x

2x² - 1 - 2x² + 2x√2 - 1 + x² - 2x√2 + 2 + 5 ≤ x² - 2x
2x² - 1 - 2x² + 2x√2 - 1 + x² - 2x√2 + 2 + 5 - x² + 2x ≤ 0
2x + 5 ≤ 0
2x ≤ -5 |:2
x ≤ -2½
(x√2 - 1) (x√2 + 1) - (x√2 - 1)² + (x - √2)² + 5 ≤ x(x - 2)

2x²-1-[(x√2)²-2√2x+1]+x²-2√2x+2+5≤x²-2x

2x²-1-2x²+2√2x-1+x²-2√2x+2+5≤x²-2x

-1-1+2+5+2x ≤ 0

2x≤-5-2+1+1

2x≤-5 |:2

x≤-2½

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