Arcsin(-1)=-pí/2, arcsin1/2= pí/6
-pí/2+pí/6=-2pí/6=-pí/3
tg(-pí/3) = -odm. ze 3 = priblizitelno -1,732........
(6х-7)²-5(2х-5)(2х+5)-2(4х-15)(2x-4)= -2
36x²-84x+49-5(4x²-25)-2(8x²-30x-16x+60)+2=0
36x²-84x+49-20x²+125-16x²+60x+32x-120+2=0
36x²-20x²-16x²-84x+60x+32x+49+125-120+2=0
8x+56=0
8x= -56
x= -7
(6*(-7)-7)²-5(2*(-7)-5)(2*(-7)+5)-2(4*(-7)-15)(2*(-7)-4)= (-42-7)²-5(-14-5)(-14+5)-2(-28-15)(-14-4)= (-49)²-5*(-19)*(-9)-2*(-43)*(-18)=2401-855-1548=2
U+v=4
3u-5v=20
u=4-v
3(4-v)-5v=20,12-3v-5v=20,12-8v=20,8v=12-20,8v=-8,v=-1
u=4-v
v=-1
u=4-(-1)=4+1=5
v=-1
/u,v/=/5,-1/
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![f(x)=\sqrt{\frac{(x-7)(x+10)}{x-2}}\\\\OOF:\; \; \; \frac{(x-7)(x+10)}{x-2}\geq 0\\\\znaki:\; \; \; ---[-10\, ]+++(2)---[\, 7\, ]+++\\\\\underline {x\in D(y)=[-10;2)\cup [\, 7;+\infty )}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%7B%5Cfrac%7B%28x-7%29%28x%2B10%29%7D%7Bx-2%7D%7D%5C%5C%5C%5COOF%3A%5C%3B%20%5C%3B%20%5C%3B%20%5Cfrac%7B%28x-7%29%28x%2B10%29%7D%7Bx-2%7D%5Cgeq%200%5C%5C%5C%5Cznaki%3A%5C%3B%20%5C%3B%20%5C%3B%20---%5B-10%5C%2C%20%5D%2B%2B%2B%282%29---%5B%5C%2C%207%5C%2C%20%5D%2B%2B%2B%5C%5C%5C%5C%5Cunderline%20%7Bx%5Cin%20D%28y%29%3D%5B-10%3B2%29%5Ccup%20%5B%5C%2C%207%3B%2B%5Cinfty%20%29%7D)
P.S Подкоренное выражение должно быть неотрицательным. Решаем неравенство методом интервалов.