(1/2)^(x²+x-2)≥4^(x-1). Created by lewtolstoytimoy. algebra-ru

2)^(x²+x-2)≥4^(x-1)...

Verified answer

(2^(-1))^(x²+x-2) ≥ (2²)^(x-1)
2^(-x²-x+2) ≥ 2^(2x-2)
-x²-x+2 ≥ 2x-2
-x²-3x+4 ≥ 0
x²+3x-4 ≤ 0
x²+3x-4 = x²+4x-x-4 = x(x-1)+4(x-1) = (x-1)(x+4)
x₁ = 1
x₂ = -4
+ - +
-----------.----------.------------>x
-4 1
x∈[-4; 1]

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lewtolstoytimoy Спасибо большое!!!

максикола

(2^(-1))^(x²+x-2) ≥ (2²)^(x-1)
2^(-x²-x+2) ≥ 2^(2x-2)
-x²-x+2 ≥ 2x-2
-x²-3x+4 ≥ 0
x²+3x-4 ≤ 0
x²+3x-4 = x²+4x-x-4 = x(x-1)+4(x-1) = (x-1)(x+4)
x₁ = 1
x₂ = -4
+ - +
-----------.----------.------------>x
-4 1
x∈[-4; 1]

0 votes Thanks 0

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