Question

Решите уравнение 7,8

Answer 1

$\sqrt{34-5x}+2x=7\\ \sqrt{34-5x}=7-2x\\ 34-5x=49-28x+4x^2\\ 4x^2-23x+15=0\\ x_1=5 \\7-2\times5<0\\ x_2=\frac{3}{4}\\ 7-\frac{3}{4}\times2>0\\ x=\frac{3}{4}$

$2\sin^22x+\cos2x-1=0\\ 2x=\alpha \\ \sin^2\beta =\frac{1-\cos2\beta}{2} \\ 1-\cos2\alpha +\cos\alpha-1=0\\ \cos\alpha =\cos2\alpha \\ \cos2x=\cos4x\\ x=\frac{\pi k}{3}$