___ ____
√x+4 =7- √2x+6
___ ____
√x+4 + √2x+6 =7
__________
x+4+2√(x+4)*(2x+6) + 2x +6=49
_____________
x+4+2√2x^2 +6x+8x+24 +2x+6=49
___________
3x+10+2√2x^2+14x+24=49
___________
2√2x^2+14x+24=49-3x-10
___________
2√2x^2+14x+24=39-3x
4(2x^2+14x+24)=1521-234x+9x^2
8x^2+56x+96-1521+234x-9x^2=0
-x^2+290x-1425=0
x^2-290x+1425
D= 290^2 - 4 *1*1425= 84100-5700=78400
x= 290+-280/2
x1= 290+280/2=285
x2= 290-280/2=5
Проверка:
_____ _________
√285+4 = 7-√2 * 285 + 6
17 = -17
___ _____
√5+4=7-√2*5+6
3=3
x≠285
x=5
Ответ: 5