Х-у=40
√х+√у=10 √х=10-√у (возводим в квадрат) х=100-2√у+у
Подставляем в первое: 100-20√у+у-у=40
-20√у=-60
√у=3 у=9
х-у=40 х-9=40
х=49
Ответ: х=49 у=9
2 • (x - 2) • (x + 2) = (x - 4) • (x + 4) + (x - 3) •(x + 3) + x
2 • (x^2 - 4) = x^2 - 16 + x^2 - 9 + x
2x^2 - 8 = 2x^2 - 25 + x
-8 = -25 + x
- x = -25 + 8
-x = -17
x = 17
@iGeniusOX⚡
x^(log(2) x) * 14^(log(2) 7) = x^(log(2) 7) * x^(log(2) 14)
ОДЗ x > 0
log (xy) = log x + log y
логарифмируем по основанию 2
log(2) (x^(log(2) x) * 14^(log(2) 7)) = log(2) (x^(log(2) 7) * x^(log(2) 14))
log(2) x^(log(2) x) + log(2) 14^(log(2) 7) = log(2) x^(log(2) 7) + log(2)(x^(log(2) 14)
(log(2) x )*(log(2) x) + (log(2) 14)* (log(2) 7) = log(2) x * (log(2) 7) + (log(2) x)*(log(2) 14)
log(2) x = t
t² - (log(2) 7 + log(2) 14)* t + log(2) 14 * log(2) 7 = 0
D = (log(2) 7 + log(2) 14)²- 4*log(2) 14 * log(2) 7 = (log(2) 14 - log(2) 7)²
t12 = [ (log(2) 14 + log(2) 7) +- (log(2) 14 - log(2) 7)]/2 = log(2) 14 и log(2) 7
1. log(2) x = log(2) 7
x = 7
2. log(2) x = log(2) 14
x = 14
ответ 7 и 14
(a-2)^2-(a+1)*(a-2)=а^2-4а+4-(а^2-2а+а-2)=а^2-4а+4-а^2+2а-а+2=-3а+6