<span>√12*(√21+√3) - 3√28 = </span>√(3*4)*(√<span>(3*7)+√3) - 3√(4*7) = </span> 2√3*(√3*<span>√7+√3) - 6√7 = </span>
= 2√3*√3*<span>√7 + </span><span>2√3*√3 - 6√7 = </span> 2*3*√7 + 2*3 - 6√7 = 6√7+ 6 - 6√7 = 6
Удачи!Если что-то не так напиши.Буду рада
<span><span><span>−3</span>,<span><span><span>5<span>x2</span></span>+<span>6x</span></span>−0</span></span>,<span>5=0</span></span>
<span>Коэффициенты уравнения: </span>
<span><span>a=<span>−3</span></span>,5</span><span>, </span><span>b=6</span><span>, </span><span><span>c=<span>−0</span></span>,5</span>
<span>Вычислим дискриминант: </span>
<span><span>D=<span><span>b2</span>−<span><span>4a</span>c</span></span></span>=</span><span><span><span><span>62</span>−<span><span>4·<span>(<span><span>−3</span>,5</span>)</span></span>·<span>(<span><span>−0</span>,5</span>)</span></span></span>=<span>36−7</span></span>=29</span>
<span>(<span>D>0</span>)</span>, следовательно это квадратное уравнение имеет 2 различных вещественных корня:
Вычислим корни:
<span><span>x<span>(<span>1,2</span>)</span></span>=<span><span><span>−b</span>±<span>√D</span></span><span>2a
</span></span></span><span><span><span><span><span><span>x1</span>=<span><span><span>−b</span>+<span>√D</span></span><span>2a</span></span></span>=<span><span><span><span>−6</span>+5</span>,385</span><span>2·<span>(<span><span>−3</span>,5</span>)</span></span></span></span>=<span><span><span>−0</span>,615</span><span>−7</span></span></span>=0</span>,088
</span><span><span><span><span><span><span>x2</span>=<span><span><span>−b</span>−<span>√D</span></span><span>2a</span></span></span>=<span><span><span><span>−6</span>−5</span>,385</span><span>2·<span>(<span><span>−3</span>,5</span>)</span></span></span></span>=<span><span><span>−11</span>,385</span><span>−7</span></span></span>=1</span>,626</span>
<span><span><span>−3</span>,<span><span><span>5<span>x2</span></span>+<span>6x</span></span>−0</span></span>,<span><span>5=<span>0.5·<span><span>(<span><span>x−0</span>,088</span>)</span><span>(<span><span>x−1</span>,626</span>)</span></span></span></span>=0
</span></span>Ответ:
<span><span><span>x1</span>=0</span>,088</span>
<span><span><span>x2</span>=1</span>,<span>626</span></span>
log(2) (4^x + 4) = x + log(2) (2^x*2^1 - 3)
log(2) (4^x + 4) = x + log(2) (2^(x+1) - 3)
ОДЗ
4^x + 4 > 0 x∈ R
2^(x+1) > 3
log(2) 2^(x+1) > log(2) 3
x + 1 > log(2) 3
x > log(2) 3 - 1 ≈ 1.59 - 1 ≈ 0.59
ОДЗ x ∈ (log(2) 3 - 1 , +∞ )
log(2) (4^x + 4) = x + log(2) (2^(x+1) - 3)
log(2) (4^x + 4) = log (2) 2^x + log(2) (2^(x+1) - 3)
log(2) (4^x + 4) = log(2) 2^x*(2*2^x - 3)
снимаем логарифмы
4^x + 4 = 2^x*(2*2^x - 3)
(2^x)^2 + 4 = 2*2^x*2^x - 3*2^x
(2^x)^2 - 3*2^x - 4 = 0
2^x = t > 0
t^2 - 3t - 4 = 0
D=9 + 16 = 25 = 5²
t₁₂ = (3 +- 5)/2 = -1 4
1. t₁ = -1
решений нет t>0
2. t=4
2^x = 4
x = 2 (входит в ОДЗ x > log(2) 3 - 1 )
ответ х=2