(m - 4p)² - (m + 4p)² m² - 16p² = ------------------------------ * ------------------ = m (m² - 16p²) -2p²
m² - 8mp + 16p² - m² - 8mp - 16p² = ------------------------------------------------ = -2mp²
-16mp 8 = ----------------- = ---------- -2mp² p
-------------------------------------------------------------------------------------- x/y + y/x = 5/2 x - y = 3 одз x≠ 0; y≠0
x/y + y/x = 5/2 y = x - 3 ------------------------------------------------------------------ x / (x -3) + (x - 3) / x = 5/2 y = x - 3 ------------------------------------------------------------------
x * x + (x - 3)(x - 3) --------------------------- = 5/2 x (x - 3)
y= x - 3 -----------------------------------------------------------------
x² + (x - 3)² ----------------- = 5/2 x² - 3x
y= x - 3 --------------------------------------------------------------
Answers & Comments
( ----------------- - ----------------) * ------------------ =
m² + 4mp m² - 4mp 2p²
m - 4p m + 4p -1 * (m² - 16p²)
= ( ------------------- - ------------------) * ---------------------- =
m(m+ 4p) m(m - 4p) 2p²
(m - 4p)(m - 4p) - (m + 4p)(m + 4p) m² - 16p²
= -------------------------------------------------- * ---------------------- =
m (m + 4p)(m - 4p) -2p²
(m - 4p)² - (m + 4p)² m² - 16p²
= ------------------------------ * ------------------ =
m (m² - 16p²) -2p²
m² - 8mp + 16p² - m² - 8mp - 16p²
= ------------------------------------------------ =
-2mp²
-16mp 8
= ----------------- = ----------
-2mp² p
--------------------------------------------------------------------------------------
x/y + y/x = 5/2
x - y = 3
одз x≠ 0; y≠0
x/y + y/x = 5/2
y = x - 3
------------------------------------------------------------------
x / (x -3) + (x - 3) / x = 5/2
y = x - 3
------------------------------------------------------------------
x * x + (x - 3)(x - 3)
--------------------------- = 5/2
x (x - 3)
y= x - 3
-----------------------------------------------------------------
x² + (x - 3)²
----------------- = 5/2
x² - 3x
y= x - 3
--------------------------------------------------------------
x² + x² - 6x + 9
-------------------- = 5/2
x² - 3x
y= x - 3
----------------------------------------------------------------
2x² - 6x + 9
------------------- = 5/2
x² - 3x
y = x - 3
--------------------------------------------------------------
2 * (2x² - 6x + 9) = 5 * (x² - 3x)
y = x - 3
-------------------------------------------------------------
4x² - 12x + 18 = 5x² - 15x
y= x - 3
-----------------------------------------------------------
5x² - 4x² - 15x + 12x - 18 = 0
y= x - 3
----------------------------------------------------------
x² - 3x - 18 = 0
y = x - 3
__________________________________
Решаем квадратное уравнение
x² - 3x - 18 = 0
D = (-3)² - 4 * 1 * (-18) = 9 + 72 = 81 > 0 ⇒ уравнение имеет 2 корня
x₁ = (3 - √81) / 2 = -6 / 2 = -3 ≠ 0 ⇒ отвечает одз
x₂ = (3 + √81) / 2 = 12 / 2 = 6 ≠ 0 ⇒ отвечает одз
___________________________________
x₁ = -3
y₁ = x - 3
x₁ = -3
y₁ = -3 -3
x₁ = -3
y₁ = -6 ≠ 0 ⇒ отвечает одз
---------------------------------------------------------------------------
x₂ = 6
y₂ = x - 3
x₂ = 6
y₂ = 6 - 3
x₂ = 6
y₂ = 3 ≠ 0 ⇒ отвечает одз
----------------------------------------------------------------------
Проверка1
-3 / (-6) + (-6) / (-3) = 5/2
-3 - (-6) = 3
1/2 + 2 = 5/2
-3 + 6 = 3
1/2 + 4/2 = 5/2
3 = 3
5/2 = 5/2
3 = 3
-----------------------------------------------------------------------
Проверка 2
6/3 + 3/6 = 5/2
6 - 3 = 3
2 + 1/2 = 5/2
3 = 3
4/2 + 1/2 = 5/2
3 = 3
5/2 = 5/2
3 = 3
-------------------------------------------------------------
x₁ = -3
y₁ = -6
x₂ = 6
y₂ = 3