1) 17 38 97
19 60 99 = 0
18 59 98
2) 8 5 3
9 7 2 = 0
6 1 5
3) 1 a b+ c
1 b c+a = 0
1 c a+ b
4) a d 3a- 4d
b e 3b- 4e = 0
c f 3c - 4f
5) x a b
a x b =(x -a)(x -b)(x+a+b)
a b x
6) a+1 2 3
3 a+2 4 prove a -1 is the factor
4 4 a+3
7) 0 a b
-a 0 c = 0
-b -c 0
8) a b c
c a b = a³+b³+c³- 3abc
b c a
9) 1+a 1 1
1 1+b 1 =abc(1/a +1/b +1/c)
1 1 1+ c
10) a-b-c 2a 2a
2b b-c-a 2b = (a+ b+ c)³
2c 2c c-a-b
11) a+ b +2c a b
c b+c+ 2a b =2(a+b+c)³
c a c+ a + 2b
12) a+ b + c -c -b
-c a+ b + c -a
-b -a a+ b + c
= 2(b+c)(c+a)(a+b)
13) a²+10 ab ac
ab b²+10 bc is divisible by 100
ac bc c²+10
14) y+z z+x x+y 2x 2y 2z
z+x x+y y+z = 2y 2z 2x
x+y y+z z+x 2z 2x 2y
15) 1 a a²-bc
1 b b²-ca = 0
1 c c²-ab
16) a b c
a² b² c²
b+c c+a a+b
=(a+ b+ c)(a- b)(b - c)(c - a)
17) y²+ z² xy zx
xy z²+ x² yz = 4x²y²z²
zx yz y²+ z²
18) x²+y²+ 1 x²+2y²+3 x²+ 3y²+4
y² +2 2y²+ 6 3y²+8 =x²y²
y²+ 1 2y² + 3 3y²+4
19) -bc bc+ b² bc+ c²
ca +a² -ca ca+ c²= (ab+bc+ca)²
ab +a² ab+ b² -ab
B) Solve by Cramer's Rule:
1) 2x - y = 1; 3x + 2y = 5. 1,1
2) x+ 2y - z = 9; 2x - y +3z = -2 ; 3x+ 2y +3z = 9. 2,3,-1
3) -x+ 2z+1 = 0 ; 2x - y -4z =2 ; y +2z = 4. 5,0,2
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