ax^4+bx^2+c=0
նշ. x^2 = t, x^4=t^2
at^2 + bt + c = 0
D= b^2 — 4 *ac [x = -2
[t = -b — VD/2a = 4 > [x^2 = 4 > [x = 2
[t = -b + VD/2a = -1 >[x^2 = 8 > [x=-V8
Պատ.՝ +-2;+-V8 [x=V8
Վ. 219
ա) x^4-3x^2+2 = 0
x^2 = t
t^2-3t+2=0
D = 9 — 4 * 1 * 2 = 9 — 8 = 1 [x = -1
[t = 3 — 1/2 = 2/2 = 1 > [x^2=1 > [x = 1
[t = 3 + 1/2 = 4/2 = 2 > [x^2=2 > [x = -V2
Պատ.՝ +-1; +-V2 [x = V2
բ) x^4 — 10x^2 + 9 = 0
t^2-10t+9 = 0
D = 100 — 4 * 1 * 9 = 100 — 36 = 64 [x = -1
[t = 10 — 8/2 = 2/2 = 1 > [x^2 = 1 > [x = 1
[t = 10 + 8/2 = 18 = 2 = 9 >[x^2 = 9 > [x = -3
Պատ.՝ +-1; +-3 [x = 3
գ) x^4 — 5x^2 + 4 = 0
t^2 — 5t + 4 = 0
D = 25 — 4 * 1 * 4 = 25 — 16 = 9 [x=1
[t = 5 — 3/2 = 2/2 = 1 > [x^2=1 > [x=-1
[t = 5 + 3/2 = 8/2 = 4 > [x^2 = 4 > [x=2
Պատ.՝ +-1;+-2 [x=-2
դ) x^4 — 26x^2 + 25 = 0
t^2 — 26t + 25 = 0
D = 676 — 4 * 1 * 25 = 676 — 100 = 576 [x = -1
[t = 26 — 24/2 = 2/2 = 1 > [x^2 = 1 > [x = 1
[t = 26 + 24/2 = 50/2 = 25 > [x^2 = 25 > [x = 5
Պատ.՝ +-1;+-5 [x = -5
ե) x^4 — 20x^2 + 64 = 0
t^2 — 20t+ 64 = 0
D = 400 — 4 * 1 * 64 = 400 — 256 = 144 [x = -2
[t = 20 — 12/2 = 8/2 = 4 > [x^2 = 4 > [x = 2
[t = 20 + 12/2 = 32/2 = 16 > [x^2 = 16 > [x = -4
Պատ.՝ +-2; +- 4 [x = 4
զ) x^4 + 20x^2 + 64
t^2 + 20t + 64 = 0
D = 400 — 4 * 1 * 64 = 400 — 256 = 144
[t = -20 — 12/2 = -32/2 = -16 չի լուծվում
[t = -20 + 12/2 = -8/2 = -4 չի լուծվում
է) x^4 — 5x^2 + 6 = 0
t^2 — 5t + 6 = 0
D = 25 — 4 * 1 * 6 = 25 — 24 = 1 [x = V2
[t = 5 — 1/2 = 4/2 = 2 > [x^2 = 2 > [x = — V2
[t = 5 + 1/2 = 6/2 = 3 > [x^2 = 3 > [x = V3
Պատ.՝ +- V2; +- V3 [x = -V3
Վարժ. 220
ա) a^4 + 2a^2 — 8 = 0
t^2 + 2t — 8 = 0
D = 4 — 4 *1 * (-8) = 4 + 32 = 36
[t = -2 — 6/2 = -8/2 = -4 >[a^2 = -4 լուծում չունի [a = V2
[t = -2 + 6/2 = 4/2 = 2 > [a^2 = 2 > [a = -V2
Պատ.՝ +- V2
բ) y^4 + 9y^2 = 400
y^4 + 9y^2 — 400 = 0
t^2 + 9t — 400= 0
D = 81 — 4 * 1 * (-400) = 81 + 1600 = 1681
[t = -9 — 41 = -50/2 = -25 L.չ. [y = 4
[t = -9 + 41 = 32/2 = 16 > [y = -4 Պատ.՝ +- 4
ե) n^4 — 2n^2 + 1 = 0
t^2 — 2t + 1 = 0
D = 4 — 4 * 1 * 1 = 4 — 4 = 0
X = 2/2 = 1 > n^2 = 1 > [n = -1
Պատ.՝ +- 1 [n = 1
Վարժ. 221
բ) x^4 — 14x^2 — 15 = 0
t^2 — 14t — 15 = 0
D = 196 — 4 * 1 * (-15) = 196 + 60 = 256
[t = 14 — 16/2 = -2/2 = -1 > [x^2 = 1 չ.լ. > [x = V15
[t = 14 + 16/2 = 30/2 = 15 > [x^2 = 15 > [x = -V15 Պատ.՝ +- V15
Դաս. 10
Արփինե Խաչատրյանի բլոգ 