10ab+(-5a+b)² = 10ab +(b-5a)² = 10ab+ b² -10ab +25a² = b²+25a²
при a=√10 и b=√5 b²+25a²=(√5)²+25(√10)² = 5+25*10 =5+250=255
(x²-4x)²-(x²-4x+4)-16≤0
(x²-4x)²-(x²-4x)-20≤0
x²-4a=a
a²-a-20≤0
a1+a2=1 U a1*a2=-20
a1=-4 u a2=5
-4≤a≤5
{x²-4x≥-4 (1)
{x²-4x≤5 (2)
(1) x²-4x+4≥0
(x-2)²≥0⇒x-любое
(2) x²-4x-5≤0
x1+x2=4 u x1*x2=-5⇒x1=-1 U x2=5
x∈[-1;5]
1. <span>2xy² - 18х = </span> 2х(<span>y² - 9) = </span> 2х(y - 3)(y + 3)
2. <span>(b-1)²(b+2) - b²(b-3) + 3</span> = (<span>b² - 2</span><span>b + 1)</span>(b+2) - <span>b³ + 3</span>b² + 3 =
= <u /><span><u>b³ +</u> 2</span>b² - 2<span>b² - 4</span>b + <span>b + 2<u /></span><u> - b³</u> + 3b² + 3 =
= - 4b + <span>b + 2</span> + 3b² + 3 = 3b² + 5<span>b + 5</span>
Sin2x=2sinx*cosx
3x=2*(3x/2)⇒sin3x=sin[2*(3x/2)]=2sin(3x/2)*cos(3x/2)