5x²-125 = 5(x²-25)=5(x-5)(x+5)
64 - 4y² = 4(16 - y²) = 4(4-y)(4+y)
ax² - ay² = a(x² - y²) = a(x - y) (x+y)
x³-xy² = x(x² - y²) = x(x - y) (x+y)
(x+y)²-z² = (x+y-z)(x+y+z)
81 - (a+2b)² = (9 - a - 2b) (9 + a + 2b)
(a+2b)² -(a-2b)² =(a+2b-a+2b)(a+2b+a-2b)=4b*2a
(c+d)²-(2c+3d)²=(c+d+2c+3d)(c+d-3c-3d)=(3c+4d)(-2c-2d) = = -2(c+d)(3c+4d)
a^2n - b^2m = (a^n - b^m)(a^n + b^m)
c^4n -d^4 =(c^2n - d^2) (c^2n + d^2)
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№ 3
4а²(х+7)+3(х+7)=(х+7)(4а²+3)
если х= 1,05 и а= –0,5, то
(1,05+7)(4·(–0,5)²+3)=8,05·(4·0,25+3)=8,05·(1+3)=8,05·4= 32,2
Ответ: 32,2
№ 4
а) = 5а²b(3+2abc)
б) = (m+n)(3–(m+n))=(m+n)(3–m–n)
в) = –6x(1–x)–(1–x)² = (1–x)(–6x–(1–x)) = (1–x)(–6x–1+x) = (1–x)(–5x–1)
г) = 2ay–b+by–2a= (2ay–2a)+(by–b) = 2a(y–1)+b(y–1) = (y–1)(2a+b)
1)
1/2+lg(3) и lg(19)-lg(2)
1+2lg(3) и 2lg(19)-2lg(2)
lg(3^2*10) и lg(19^2/2^2)
lg(90) и lg(90,25)
lg(90) < lg(90,25) значит (1/2+lg(3)) < (lg(19)-lg(2))
2)
(lg(5)+lg( корень(7)) ) /2 и lg( (5+корень(7)) /2)
(lg(5)+lg( корень(7)) ) и 2lg( (5+корень(7)) /2)
5*корень(7) и ( (5+корень(7)) /2)^2
5*корень(7) и ( (25+7+10*корень(7)) /2^2
5*корень(7) и ( (32+10*корень(7)) /2^2
10*корень(7) и ( (16+5*корень(7))
5*корень(7) и 16
25*7 и 16*16
175 и 256
175 < 256 значит {(lg(5)+lg( корень(7)) ) /2} < {lg( (5+корень(7)) /2)}
3)
3*(lg(7)-lg(5)) и lg9 - 2/3*lg(8)
(lg(7/5)^3) и lg(9/8^(2/3))
(lg(7/5)^3) и lg(9/4)
(7/5)^3 и (9/4)
7^3*4 и 9*5^3
1372 и
1125
1372 >
1125 значит {3*(lg(7)-lg(5))} > {lg9 - 2/3*lg(8)}
4)
lglglg(50) и (lg(50))^3
lg(50)=lg(10)+lg(5) = 1+ lg(5) > 1
(lg(50))^3=(1+ lg(5))^3 > 1
lg(50)<lg(100)=2
lg(50) <2
lglg(50) <lg2<lg(10)=1
lglg(50) <1
lglglg(50) <lg1=0
lglglg(50) < 0
(lg(50))^3 > 1
значит lglglg(50) < (lg(50))^3