а) х2+5х-14=(х-2)(х+7);
х2+5х-14=0;
д=25-4*(-14)=25+56=81;
х1=(-5+9)/2=4/2=2;
х2=(-5-9)/2=-14/2=-7;
б)16х2-14х+3=16(х-0,5)(х-0,375);
16х2-14х+3=0
д=(-14)2-4*16*3=196-192=4;
х1=(14+2)/32=16/32=0,5;
х2=(14-2)/32=12/32=0,375;
в)(3у2-7у-6)/(4-9у2)=3(у-3)(у+2/3)/-9(у-2/3)(у+2/3)=3(у-3)/(6-9у)=
(3у-9)/(6-9у)=3(у-3)/3(2-3у)=(у-3)/(2-3у);
3у2-7у-6=(у-3)(у+2/3);
3у2-7у-6=0
д=49-4*3*(-6)=49+72=121;
у1=(7+11)/6=18/6=3;
у2=(7-11)/6=-4/6=-2/3;
4-9у2=-9(у-2/3)(у+2/3);
4-9у2=0
9у2=4
у1=4/9=2/3;
у2=-2/3.
а) х2+5х-14=(х-2)(х+7);
х2+5х-14=0;
д=25-4*(-14)=25+56=81;
х1=(-5+9)/2=4/2=2;
х2=(-5-9)/2=-14/2=-7;
б)16х2-14х+3=16(х-0,5)(х-0,375);
16х2-14х+3=0
д=(-14)2-4*16*3=196-192=4;
х1=(14+2)/32=16/32=0,5;
х2=(14-2)/32=12/32=0,375;
в)(3у2-7у-6)/(4-9у2)=3(у-3)(у+2/3)/-9(у-2/3)(у+2/3)=3(у-3)/(6-9у)=
(3у-9)/(6-9у)=3(у-3)/3(2-3у)=(у-3)/(2-3у);
3у2-7у-6=(у-3)(у+2/3);
3у2-7у-6=0
д=49-4*3*(-6)=49+72=121;
у1=(7+11)/6=18/6=3;
у2=(7-11)/6=-4/6=-2/3;
4-9у2=-9(у-2/3)(у+2/3);
4-9у2=0
9у2=4
у1=4/9=2/3;
у2=-2/3.
1) 2cosx-1 < 0
cosx < 1/2
arccos(1/2) + 2πn < x < 2π - arccos(1/2) + 2πn, n ∈ Z
π/3 + 2πn < x < 2π - π/3 + 2πn, n ∈ Z
π/3 + 2πn < x < 5π/3 + 2πn, n ∈ Z
2) sin2x - √2/2 < 0
sin2x < √2/2
- π - arcsin(√2/2) + 2πk < 2x < arcsin(√2/2) + 2πk, k ∈ Z
- π - π/4 + 2πk < 2x < π/4 + 2πk, k ∈ Z
- 5π/4 + 2πk < 2x < π/4 + 2πk, k ∈ Z
- 5π/8 + πk < x < π/8 + πk, k ∈ Z
3) tgx<1
- π/2 + πn < x < arctg(1) + πn, n ∈ Z
- π/2 + πn < x < π/4 + πn, n ∈ Z