Log2 (2x-1) + log2(x+5) = log2 13
(2x -1)(x+5) = 13
2x² +9x -5 -13=0
2x² +9x -18 = 0
D = 81 -4·2·(-18) = 81 + 144=225
x1 =(-9+15)/4 = 6/4= 3/2 = 1,5
х2 = (-9-15)/4 = -6
Теперь ОДЗ: 2х -1>0 ⇒ x > 1/2
x +5 > 0⇒x > -5
ОДЗ : х > 1/2
Ответ:1,5
Скорость автобуса х
автомоб х+20
120/х-1=120/(х+20)
-х^2-2x+240=0
х=14,52
Ответ 14,52 км/ч и 24,52 км/ч
![\frac{ (a+b)^{2}- (ab+1)^{2} }{( a^{2} -1)( b^{2} -1)} = \frac{( a^{2}+2ab+ b^{2})-( a^{2} b^{2} +2ab+1)}{( a^{2}-1)( b^{2} -1) } = \frac{ a^{2}+ b^{2} - a^{2}b^{2}-1 }{( a^{2} -1)(b^{2} -1)} =](https://tex.z-dn.net/?f=+%5Cfrac%7B+%28a%2Bb%29%5E%7B2%7D-+%28ab%2B1%29%5E%7B2%7D++%7D%7B%28+a%5E%7B2%7D+-1%29%28+b%5E%7B2%7D+-1%29%7D+%3D+%5Cfrac%7B%28+a%5E%7B2%7D%2B2ab%2B+b%5E%7B2%7D%29-%28+a%5E%7B2%7D++b%5E%7B2%7D+%2B2ab%2B1%29%7D%7B%28+a%5E%7B2%7D-1%29%28+b%5E%7B2%7D+-1%29+%7D+%3D++%5Cfrac%7B+a%5E%7B2%7D%2B+b%5E%7B2%7D+-+a%5E%7B2%7Db%5E%7B2%7D-1+%7D%7B%28+a%5E%7B2%7D+-1%29%28b%5E%7B2%7D+-1%29%7D+%3D+)
![\frac{( a^{2} -1)-( a^{2}b^{2} - b^{2} )}{( a^{2} -1)(b^{2} -1)} = \frac{( a^{2} -1)- b^{2} ( a^{2} -1)}{( a^{2} -1)( b^{2} -1)} = \frac{( a^{2} -1)(1- b^{2} )}{( a^{2} -1)( b^{2} -1)} = \frac{1- b^{2} }{ b^{2} -1} = -\frac{b^{2} -1}{b^{2} -1} =-1](https://tex.z-dn.net/?f=+%5Cfrac%7B%28+a%5E%7B2%7D+-1%29-%28+a%5E%7B2%7Db%5E%7B2%7D+-+b%5E%7B2%7D+%29%7D%7B%28+a%5E%7B2%7D+-1%29%28b%5E%7B2%7D+-1%29%7D+%3D+%5Cfrac%7B%28+a%5E%7B2%7D+-1%29-+b%5E%7B2%7D+%28+a%5E%7B2%7D+-1%29%7D%7B%28+a%5E%7B2%7D+-1%29%28+b%5E%7B2%7D+-1%29%7D+%3D+%5Cfrac%7B%28+a%5E%7B2%7D+-1%29%281-+b%5E%7B2%7D+%29%7D%7B%28+a%5E%7B2%7D+-1%29%28+b%5E%7B2%7D+-1%29%7D+%3D+%5Cfrac%7B1-+b%5E%7B2%7D+%7D%7B+b%5E%7B2%7D+-1%7D+%3D+-%5Cfrac%7Bb%5E%7B2%7D+-1%7D%7Bb%5E%7B2%7D+-1%7D+%3D-1)
Ответ: - 1 при любых значениях переменных a и b,
А-7√а/а-49=√а(√а-7)/(√а-7)(√а+7)=√а/√а+7