Վարժ․ 217
ա) x4=(x2)2
բ) a6=(a3)2
գ) y8=(y4)2
դ) m10=(m5)2
Վարժ․ 218
ա) x4+2x2+1=0
x2=a
a2+2a+1=0
բ) m4-3+2m2=0
m4-2m2+3=0
m2=a
a2+2a-3=0
գ) 4y2-7y4=0
-7y4-4y2=0
y2=a
-7a2+4a=0
դ) 15-x4+2x2=0
-x4+2x2-15=0
x2=a
-a2+2a-15=0
ե) x6-3x3+2=0
x3=a
a2-3a+2=0
զ) y8-4=0
y4=a
a2-4=0
Վարժ․ 219
ա) x4-3×2+2=0
x2=a
a2-3a+2=0
D=9-8=1
[ a=3-1/2; a=3+1/2=> [ a=2/2; a=4/2=> [ a=1; a=2=> [x2=1; x2=2=> [ x=1; -1; x=√2; -√2
Պատ՝․ ±1; ±√2
բ) x4-10x2+9=0
x2=a
a2-10a+9=0
D=100-36=64
[ a=10-8/2; a=10+8/2=> [ a=2/2; a=18/2=> [ a=1; a=9=> [ x2=1; x2=9=> [ x=1; -1; x=3; -3
Պատ՝․ ±1; ±3
գ) x4-5x2+4=0
x2=a
a2-5a+4=0
D=25-16=9
[ a=5-3/2; a=5+3/2=> [ a=2/2; a=8/2=> [ a=1; a=4=> [ x2=1; x2=4=> [ x=1; -1; x=2; -2
Պատ՝․ ±1; ±2
դ) x4-26x2+25=0
x2=a
a2-26a+25=0
D=676-100= 576
[ a=26-24/2; a=26+24/2=> [ a=2/2; a=50/2=> [ a=1; a=25=> [ x2=1; x2=25=> [ x=1; -1; x=5; -5
Պատ՝․ ±1; ±5
ե) x4-20x2+64=0
x2=a
a2-20a+64=0
D=400-256=144
[ a=20-12/2; a=20+12/2=> [ a=8/2; a=32/2=> [ a=4; a=16=> [ x2=2; x2=16=> [ x=2; -2; x=4; -4
Պատ՝․ ±2; ±4
զ) x4+20x2+64=0
x2=a
a2+20a+64=0
D=400-256=144
[ a=20-12/2; a=20+12/2=> [ a=8/2; a=32/2=> [ a=4; a=16=> [ x2=4; x2=16=> [ x=2; -2; x=4; -4
Պատ՝․ ±2; ±4
է) x4-5x2+6=0
x2=a
a2-5a+6=0
D=25-24=1
[ a=5-1/2; a=5+1/2=> [ a=4/2; a=6/2=> [ a=2; a=3=> [ x2=2; x2=3=> [ x=√2; -√2; x=√3; -√3
Պատ՝․ ±√2; ±√3
ը) x4-41x2+100=0
x2=a
a2-41a+100=0
D=1681-400=1281
[ a=41-√1281/2; a=41+√1281/2=> [ x2=41-√1281/2; x2=41+√1281/2=> [ x=√(41-√1281/2); -√(41-√1281/2); x=√(41+√1281/2); -√(41+√1281/2)
Պատ՝․ ±√(41-√1281/2); ±√(41+√1281/2)
թ) 3x4-5x2+2=0
x2=a
3a2-5a+2=0
D=25-24=1
[ a=5-1/6; a=5+1/6=> [ a=4/6; a=6/6=> [ a=2/3; a=1=> [ x2=2/3; x2=1=> [ x=√2/3; -√2/3; x=1; -1
Պատ՝․ ±√2/3; ±1
ժ) 25x4-25x2+6=0
x2=a
25a2-25a+6=0
D=625-600=25
[ a=25-5/50; a=25+5=/50=> [ a=20/50; a=30/50=> [ a=2/5; a=3/5=> [ x2=2/5; x2=3/5=> [ x=√2/5; -√2/5; x=√3/5; -√3/5
Պատ՝․ ±√2/5; ±√3/5
Վարժ․ 220
ա) a4+2a2-8=0
a2=x
x2+2x-8=0
D=4-(-32)=36
[ x= -2-6/2; x= -2+6/2=> [ x= -8/2; x=4/2=> [ x= -4; x=2=> [ a2= -4; a2=2=> [ a=Ø; a=√2; -√2
Պատ՝․ ±√2
բ) y4+9y2=400
y2=a
a2+9a-400=0
D=81-(-1600)=1681
[ a= -9-41/2; a= -9+41/2=> [ a=-50/2; a=32/2=> [ a= -25; a=16=> [ y2= -25; y2=16=> [ y=Ø; y=4; -4
Պատ՝․ ±4
գ) k4=12k2+64
k2=a
k4-12k2-64=0
a2-12a-64=0
D=144-(-256)=400
[ a=12-20/2; a=12+20/2=> [ a=-8/2; 32/2=> [ a=-4; a=16=> [ k2= -4; k2=16=> [ k=Ø; k=4; -4
Պատ՝․ ±4
դ) m4=21m2+100
m2=a
a2-21a-100=0
D=441-(-400)=841
[ a=21-29/2; a=21+29/2=> [ a= -8/2; a=50/2=> [ a= -4; a=25=> [ m2= -4; m2=25=> [ m=Ø; m=5; -5
Պատ՝․ ±5
ե) n4-2n2+1=0
n2=a
a2-2a+1=0
D=4-4=0
[ a= -b/2=> [ a=2/2=> [ a=1=> [ n2=1=> [ n=1; -1
Պատ՝․ ±1
զ) 9x4-24x2+16=0
x2=a
9a2-24a+16=0
D=576-576=0
[ a= -b/2=> [ a=24/18=> [ a=4/3=> [ x2=4/3=> [ x=2/√3; x= -2/√3=> [ x= -2√3/3; 2√3/3
Պատ՝․ ±(2√3)/3
է) 6c4-35=11c2
c2=a
6a2-11a-35=0
D=121-(-840)=961
[ a=11-31/12; a=11+31/12=> [ a= -20/12; a=42/12=> [ a= -5/3; a=42/12=> [ c2=-5/3; c2=42/12=> [ c=Ø; c=√42/12; -√42/12
Պատ՝․ ±√42/12
ը) 10p4-21=p2
p2=a
10a2-a-21=0
D=2-(-840)=842
[ a=1-√842/20; a=1+√842/20=> [ p2=1-√842/20; p2=1+√842/20=> [ p=√(1-√842/20); -√(1-√842/20); p=√(1+√842/20); -√(1+√842/20)
Պատ՝․ ±√(1-√842/20); ±√(1+√842/20)
Վարժ․ 221
ա) x4+6x2+9=0
x2=a
a2+6a+9=0
D=36-36=0
a= -6/2= -3=> x2= -3=> x=Ø
Պատ՝․ Ø
բ) x4-14x2-15=0
x2=a
a2-14a-15=0
D=196-(-60)=256
[ a=14-16/2; a=14+16/2=> [ a= -2/2; a=30/2=> [ a= -1; a=15=> [ x2= -1 (Ø); x2=15=> [ x=√15; x= -√15
Պատ՝․ √15; -√15
գ) 25x4+30x2+9=0
x2=a
25a2+30a+9=0
D=900-900=0
a= -30/50= -3/5=> x2= -3/5=> x=Ø
Պատ՝․ Ø
դ) 7x4-9x2+3=0
x2=a
7a2-9a+3=0
D=81-84= -3=> Ø
Պատ՝․ Ø
ե) 9x4=9x2-1
9x4-9x2+1=0
x2=a
9a2-9a+1=0
D=81-36=45
[ a=9-√45/18; a=9+√45/18=> [ x2=9-√45/18; x2=9+√45/18=> [ x=√(9-√45/18); x= -√(9-√45/18); x=√(9+√45/18); x= -√(9+√45/18)
Պատ՝․ ±√(9-√45/18); ±√(9+√45/18)
զ) x4=30x2-36
x4-30x2+36=0
x2=a
a2-30a+36=0
D=900-144=756
[ a=30-√756/2; a=30+√756/2=> [ x2=30-√756/2; x2=30+√756/2=> [ x=√(30-√756/2); x= -√(30-√756/2); x=√(30+√756/2); x= -√(30+√756/2)
Պատ՝․ ±√(30-√756/2); ±√(30+√756/2)
է) 4x4=5x2+6
4x4-5x2-6=0
x2=a
4a2-5a-6=0
D=25-(-96)=25+96=121
[ a=5-11/8; a=5+11/8=> [ a= -6/8= -3/4; a=16/8=> [ a= -3/4; a=2=> [ x2= -3/4 (Ø); x2=2=> [ x=√2; x= -√2
Պատ՝․ ±√2
ը) x4-x2-4=0
x2=a
a2-a-4=0
D=1-(-16)=1+16=17
[ a=1-√17/2; a=1+√17/2=> [ x2=1-√17/2; x2=1+√17/2=> [ x=√(1-√17/2); x= -√(1-√17/2); x=√(1+√17/2); x= -√(1+√17/2)
Պատ՝․ ±√(1-√17/2); ±√(1+√17/2)
թ) 3-2x4=11x2
-2x4-11x2+3=0
x2=a
-2a2-11a+3=0
D=121-(-24)=121+24=145
[ a=11-√145/(-4); a=11+√145/(-4)=> [ x2=11-√145/(-4); x2=11+√145/(-4)=> [ x=√(11-√145/(-4)); x= -√(11-√145/(-4)); x=√(11+√145/(-4)); x= -√(11-√145/(-4))
Պատ՝․ ±√(11-√145/(-4)); ±√(11+√145/(-4))
ժ) 3x4+21=4x2
3x4-4x2+21=0
x2=a
3a2-4a+21=0
D=16-252= -236=> Ø
Պատ՝․ Ø
ի) x4-1=0
x2=a
a2-1=0
D=0-(-4)=4
[ a=0-2/2; a=0+2/2=> [ a= -2/2; a=2/2=> [ a= -1; a=1=> [ x2= -1 (Ø); x2=1=> [ x=1; x= -1
Պատ՝․ ±1
լ) x4+1=0
x2=a
a2+1=0
D=0-4= -4=> Ø
Պատ՝․ Ø
խ) x8+16=0
x4=a
a2+16=0
D=0-64= -64=> Ø
Պատ՝․ Ø
ծ) x8-16=0
x4=a
a2-16=0
D=0-(-64)=64
[ a=0-8/2; a=0+8/2=> [ a= -8/2; a=8/2=> [ a= -4; a=4=> [ x2= -2 (Ø); x2=2=> [ x=√2; x= -√2
Պատ՝․ ±√2
Դավիթ Մուրադյան 