Կրկնություն

451.

ա) a(x + y) + b(x + y) = (x + y)(a + b)
բ) a(x + y) – b(x + y) = (x + y)(a – b)
գ) 2x(3p – q) – (3p – q) = (3p – q)(2x – 1)
դ) m(x + y) – x – y = m(x + y) + (x + y) = (x + y)(m + 1)
ե) n(x – y) – x + y = n(x – y) + (x – y) = (x – y)(n + 1)
զ) ax + ay + (bx + by) = a(x + y) + b(x + y) = (x + y)(a + b)
է) ac + ad – bc – bd = a(c + d) – b(c – d) = (c – d)(a – b)
ը) ac – cx + a – x = c(a – x) + (a – x) = (a – x)(c + 1)
թ) ax – a + x – 1 = a(x – 1) + (x – 1) = (x – 1)(a + 1)
ժ) 2ax – 3bx – 2ay + 3by = 2a(x – y) + 3b(-x + y) = (x – y)(2a – 3b)
ի) ax – bx + cx + ay – by + cy
լ) 2ax – 5ay + a – 2bx + 5by – b

452.

ա) x³ – 6x
բ) x – 5x³
գ) 3x² – 25 = (✓3x – 5)(✓3x + 5)
դ) x² – 2 = (x – ✓2)(x + ✓2)
ե) 2x² + 8x – 7 = 2(x² – 4x – 3,5)
զ) 3x² – 5x + 2
է) 3x² – 6x – 12 = 3(x² – 2x – 4) = 3((x – 1)² – 5)
ը) 8x³ + 54x + 36x² + 27 = (2x + 3)³

615.

ա) y = √(x – 7)
x – 7 ≥ 0
x ≥ 7

բ) y = 2 + √(12 – x)
12 – x ≥ 0
x ≤ 12

գ) y = √(1 – 3x)
1 – 3x ≥ 0
3x ≤ 1
x ≤ 1/3

դ) y = 3/√(2x + 7)
2x + 7 > 0
2x > -7
x > -7/2

616.

ա) y = √(x + 1)
x + 1 ≥ 0
x ≥ -1

բ) y = √(3 – 2x)
3 – 2x ≥ 0
2x ≤ 3
x ≤ 3/2

գ) y = √x + √(x – 1)
x ≥ 0
x – 1 ≥ 0
x ≥ 1

դ) y = √(3 + 4x) + √(7x – 5)
3 + 4x ≥ 0
4x ≥ -3
x ≥ -3/4
7x – 5 ≥ 0
7x ≥ 5
x ≥ 5/7

617.

ա) y = 1/√(x – 5)
x – 5 > 0
x > 5

բ) y = x/(x + 6) – 3x/(3 – 7x)
x + 6 ≠ 0
x ≠ -6
3 – 7x ≠ 0
-7x ≠ -3
x ≠ 3/7

գ) y = √(4 – 3x) + 1/2x
4 – 3x ≥ 0
3x ≤ 4
x ≤ 4/3
2x ≠ 0
x ≠ 0

դ) y = (x – 5)/(3x – 1) + √(5 – x)
3x – 1 ≠ 0
3x ≠ 1
x ≠ 1/3
5 – x ≥ 0
x ≤ 5

ե) y = √(2x – 3)
2x – 3 ≥ 0
2x ≥ 3
x ≥ 3/2

զ) y = √(3x + 5)
3x + 5 ≥ 0
3x ≥ -5
x ≥ -5/3

է) y = √(x² – 1)
x² – 1 ≥ 0
(x – 1)(x + 1) ≥ 0
x ≥ 1
x ≤ -1

ը) y = √(x² + 5)