1) (корень из 8а - корень из а/2), умножаем на 2, ранво, 2 корень из 8а - корень из а/2=4 корень из 2а - корень из а-2
2) (8 * корень из а/2 + корень из 2а), умножаем на 2=8 корень из а + 2 корень из 2а/2
3) 4 корень из 2а - корень из а-2 минус 8 корень из а + 2 корень из 2а/2=2 корень из 2а - 9 корень из а/2, двойки сокращаются=корень из 2а - 9 корень из а.
5x-3=7x-19
2x=16
x=8
подавляем значение x в первое уравнение и находим y
y=5*8-3
y=37
Ответ: <span>точку пересечения графиков функции</span> (8;37)
<span>f′(x)=<span><span>(<span><span>sin<span>(x)</span>+cos<span>(x)/</span></span><span>sin<span>(x)</span>−cos<span>(x)</span></span></span>)</span>′</span>=</span><span><span>=<span><span><span><span>(<span>sin<span>(x)</span>+cos<span>(x)</span></span>)</span>′</span>⋅<span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)</span>−<span>(<span>sin<span>(x)</span>+cos<span>(x)</span></span>)</span>⋅<span><span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)</span>′/</span></span><span><span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)^</span>2</span></span></span>=</span><span>=<span><span><span><span>(<span><span><span>(<span>sin<span>(x)</span></span>)</span>′</span>+<span><span>(<span>cos<span>(x)</span></span>)</span>′</span></span>)</span>⋅<span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)</span>−<span>(<span>sin<span>(x)</span>+cos<span>(x)</span></span>)</span></span><span>⋅<span>(<span><span><span>(<span>sin<span>(x)</span></span>)</span>′</span>−<span><span>(<span>cos<span>(x)</span></span>)</span>′</span></span>)/</span></span></span><span><span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)^</span>2</span></span>=</span><span>=<span><span><span><span>(<span>cos<span>(x)</span>+<span>(<span>−sin<span>(x)</span></span>)</span></span>)</span>⋅<span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)</span>−<span>(<span>sin<span>(x)</span>+cos<span>(x)</span></span>)</span></span><span>⋅<span>(<span>cos<span>(x)</span>−<span>(<span>−sin<span>(x)</span></span>)</span></span>)/</span></span></span><span><span>(<span>sin<span>(x)</span>−cos<span>(x)</span></span>)^</span><span>2</span></span></span></span>
<span>x^2 + 10x + 22 = 0</span>
D = 10^2 - 4*22 = 100 - 88 = 12
√D = √4*3 = 2√3
x₁ = ( - 10 + 2√3)/2 = - 5 + √3
x₂ = ( - 10 - 2√3)/2 = - 5 - √3
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