2x^2 - 10 = 30 - 10x
2x^2 + 10x - 40 = 0
x^2 + 5x - 20 =0
Дискр= 25 + 4*20 = 105
x = -5 +- корень из 105 / 2
1) b3=b1*q^2
b2=b1*q
b5=b1*q^4
b1*b1*q^2=1/2. b1*q*b1*q^4=4;
(b1)^2*q^2=1/2, (b1)^2*q^5=4;
q^3=8;
q=2
2) b4=b1*q^3
b6=b1*q^5
b1*b1*q^3=9, b1*q*b1*q^5=1/3;
q^3=1/27;
q=1/3
1) <u>2+√5 </u>= <u>(2+√5)√5</u> =<u> 2√5 +5 </u>
√5 √5*√5 5
2) Так как 6 - √7 >0, то |6-√7|=6-√7
3)
1. (a-1)² -(a-2)(a+2) =a²-2a+1-(a²-4)=a²-2a+1-a²+4=5-2a
2. (x+y+2)(x+y-2)=(x+y)² -2² = x²+2xy+y² -4
28.29.y=sin(3x-9);⇒y¹3·cos(3x-9);
y=cos(π/3-4x);⇒y¹=(-4)·(-sin(π/3-4x))=4sin(π/3-4x);
y=cos(9x-10);⇒y¹=9(-sin(9x-10))=-9sin(9x-10);
y=sin(5-3x)⇒y¹=-3cos(5-3x);
28.30.y=√(15-7x)=(15-7x)^(1/2);⇒
y¹=(-7)·1/2·(15-7x)¹/²⁻¹=-7/2·(15-7x)⁻¹/²=-7/(2·√(15-7x));
y=√(42+0.5x);⇒y¹=1/2·0.5·(42+0.5x)⁻¹/²=1/(4·√(42+0.5x);
y=√(4+9x);⇒y¹=9·1/2·(4+9x)⁻¹/²=9/(2·√(4+9x));
y=√(50-0.2x)⇒y¹=(-0.2)·1/2·(50-0.2x)⁻¹/²=-1/(10·√(500.2x));
28.31y=(3x-2)⁷;x₀=3⇒
f¹(x)=3·(3x-7)⁶;f¹(x₀)=3·(3·3-7)⁶=3·(2)⁶=3·64=192;
28.32.y=(2x+1)⁵;x₀=-1;
f¹(x)=2·5(2x+1)⁴=10(2x+4)⁴;
f¹(x₀)=10(-2+4)⁴=10·2⁴=160;