( 2 - х )^2 - х( х + 1,5 ) = 4
4 - 4х + х^2 - х^2 - 1,5х = 4
- 5,5х = 0
х = 0
X^2 - 3x / 8 = 0 | * 8
x^2 - 3x = 0
x(x - 3) = 0
x = 0 или x - 3 = 0, x = 3
Ответ: 0; 3
Решение
По
теореме Виета имеем: x₁ + x₂ = 2<span>n
</span>x₁ * x₂ = 22n² + 8<span>n
</span><span>x₁² +
x₂² = (x₁+ x₂)² – 2x₁*x₂ = (2n)² – 2*(22n² + 8n) =
</span>= 4n² – 44n² – 16n = - 40n² – 16<span>n
</span>f(n) = - 40n² – 16<span>n
</span><span>f `(n) =
- 80n - 16
</span><span>- 80n –
16 = 0
</span><span>80n = -
16
</span><span>n= - 1/5
</span>D = 4n² – 4*(22n² + 8n) = 4n² – 88n² – 32n = - 84n²<span> – 32n
</span>- 84n²<span> –
32n > 0
</span><span>- 4n(21n
+ 8) > 0
</span><span>4n(21n +
8) < 0
</span><span>4n(21n +
8) = 0
</span>n₁ <span>= 0
</span>21n<span> + 8 = 0
</span>n₂ = - 8/21
<span>
+ - +
</span>----------------------------------à<span>
-8/21 0 </span>x<span>
</span>- 1/5 ∈ [- 8/21; 0]
<span>при значении параметра n = - 1/5 сумма квадратов корней
уравнения x</span>² <span>− 2nx + 22n</span>² <span>+ 8n = 0 будет наибольшей</span>
Ответ: n = - 1/5