![\sqrt{x+7}+ \sqrt{x-2}=9](https://tex.z-dn.net/?f=+%5Csqrt%7Bx%2B7%7D%2B+%5Csqrt%7Bx-2%7D%3D9)
ОДЗ:
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{x+7≥0 {x≥-7 ---[-7]-------------------->
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{x-2≥0 {x≥2 -------------[2]----------->
x≥2
![(\sqrt{x+7}+ \sqrt{x-2})^2=9^2 \\ x+7+x-2+2 \sqrt{(x+7)(x-2)}=81 \\ 2 \sqrt{(x+7)(x-2)}=81-5-2x \\2 \sqrt{(x+7)(x-2)}=76-2x|:2 \\ \sqrt{(x+7)(x-2)}=38-x \\ \left \{ {{38-x \geq 0} \atop {(\sqrt{(x+7)(x-2)})^2=(38-x)^2}} \right. \\ \left \{ {{x \leq 38} \atop {x^2+7x-2x-14=1444+x^2-76x}} \right. \\ \left \{ {{x \leq 38} \atop {5x+76x=1444+14}} \right. \\ \left \{ {{x \leq 38} \atop {81x=1458}} \right. \\ \left \{ {{x \leq 38} \atop {x=18}} \right.](https://tex.z-dn.net/?f=%28%5Csqrt%7Bx%2B7%7D%2B+%5Csqrt%7Bx-2%7D%29%5E2%3D9%5E2+%5C%5C+x%2B7%2Bx-2%2B2+%5Csqrt%7B%28x%2B7%29%28x-2%29%7D%3D81+%5C%5C+2+%5Csqrt%7B%28x%2B7%29%28x-2%29%7D%3D81-5-2x+%5C%5C2+%5Csqrt%7B%28x%2B7%29%28x-2%29%7D%3D76-2x%7C%3A2+%5C%5C+%5Csqrt%7B%28x%2B7%29%28x-2%29%7D%3D38-x+%5C%5C+%5Cleft+%5C%7B+%7B%7B38-x+%5Cgeq+0%7D+%5Catop+%7B%28%5Csqrt%7B%28x%2B7%29%28x-2%29%7D%29%5E2%3D%2838-x%29%5E2%7D%7D+%5Cright.+%5C%5C+%5Cleft+%5C%7B+%7B%7Bx+%5Cleq+38%7D+%5Catop+%7Bx%5E2%2B7x-2x-14%3D1444%2Bx%5E2-76x%7D%7D+%5Cright.+%5C%5C+%5Cleft+%5C%7B+%7B%7Bx+%5Cleq+38%7D+%5Catop+%7B5x%2B76x%3D1444%2B14%7D%7D+%5Cright.+%5C%5C+%5Cleft+%5C%7B+%7B%7Bx+%5Cleq+38%7D+%5Catop+%7B81x%3D1458%7D%7D+%5Cright.+%5C%5C+%5Cleft+%5C%7B+%7B%7Bx+%5Cleq+38%7D+%5Catop+%7Bx%3D18%7D%7D+%5Cright.+)
Ответ: х=18
X^2=18; x1=-кор(18)=-3кор(2); x2=3кор(2);
6+7х=3х^3
-3х^2+7х+6=0
3х^2-7х-6=0
Д = 49+4÷3×6=121
Х1= (7+11)/2= 9
Х2=(7-11)/2=-2
1.44х^2-12ху+ру^2=(1.2х-5у)^2 т.к
общая формула (х-у)^2=х^2-2ху+у^2