log²(2) x + log(2) y - 2log²(2) x = 0
9x²y - xy² = 64
x,y > 0
разложим первое
log(2) x = a
log(2) y = b
a² + b - 2b² = (a - b)(a + 2b)
D=b² + 8b² = 9b²
a12= (-b+-3b)/2 = b -2b
(log(2) x - log(2) y)(log(2)x + 2log(2) y) = 0
произведение = 0, значит один из множителей = 0
1. log(2) x - log(2) y = 0
log(2) x = log(2) y
x = y подставляем во 2
9x²x - xx² = 64
8x³ = 64
x³ = 8
x = 2
y = 2
2. log(2)x + 2log(2) y = 0
log(2)x + log(2) y² = 0
log(2) xy² = 0
xy² = 1
x = 1/y²
9x²y - xy² = 64
9(1/y²)² y - 1/y² * y² = 64
9y³ - 1 = 64
y³ = 65/9
y = ∛(65/9)
x = 1/∛(65/9)² = ∛(81/4225)
Пошаговое объяснение:log²(2) x + log(2) y - 2log²(2) x = 0
9x²y - xy² = 64
x,y > 0
разложим первое
log(2) x = a
log(2) y = b
a² + b - 2b² = (a - b)(a + 2b)
D=b² + 8b² = 9b²
a12= (-b+-3b)/2 = b -2b
(log(2) x - log(2) y)(log(2)x + 2log(2) y) = 0
произведение = 0, значит один из множителей = 0
1. log(2) x - log(2) y = 0
log(2) x = log(2) y
x = y подставляем во 2
9x²x - xx² = 64
8x³ = 64
x³ = 8
x = 2
y = 2
2. log(2)x + 2log(2) y = 0
log(2)x + log(2) y² = 0
log(2) xy² = 0
xy² = 1
x = 1/y²
9x²y - xy² = 64
9(1/y²)² y - 1/y² * y² = 64
9y³ - 1 = 64
y³ = 65/9
y = ∛(65/9)
x = 1/∛(65/9)² = ∛(81/4225)
(7/12 - 8/15)/2 + 4/5 * (7/10 - 9/16) =
Сначала вычисляем в скобках - НОК(12,15) = 60.
(35 - 32)/60 = 3/60 = 1/20.
НОК(10,16) = 80.
(56 - 45)/80 = 11/80.
1/20 : 2 + 4/5 * 11/80 =
НОК(40,100) = 200
1/40 + 11/100 = (5+22)/200 = 27/200 - ОТВЕТ