Question

решите уравнение;подробное решение
1)121-x^2=0
2)18x+6x^2=0
3)11x^2-12=0
4)x^2-9x+10=0
5)3x^2-7x+5=0
6)-2x^2+8x+5=0

Answer 1

1) $121- x^{2} =0 \ - x^{2} =-121\ x^{2} =121\x= sqrt{121} \x_{1} = 11\ x_{2} = -11$ 

2) $18x+6 x^{2} =0\6x(3+x)=0\x=0\3+x=0\x=-3$

3) $11 x^{2} -12=0\11 x^{2} =12\ x^{2} = frac{12}{11} \ x_{1} = sqrt{ frac{12}{11} } = sqrt{1 frac{1}{11} } \ x_{2} =- sqrt{ frac{12}{11} }=- sqrt{1 frac{1}{11} }$

4) $x^{2} -9x+10=0\ D= b^{2} -4ac\D= 9^{2} -4*10=41\ x_{1}= frac{-b+ sqrt{D} }{2a}= frac{9+ sqrt{41} }{2} \ x_{2} = frac{-b- sqrt{D} }{2a} = frac{9- sqrt{41} }{2}$

5) $3 x^{2} -7x+5=0\D=7^{2} -4*5*3=49-60=-11$ 
Корней нет

6) $-2 x^{2} +8x+5=0\2 x^{2} -8x-5=0\D=8^{2} -4*(-5)*2=64-40=24\ x_{1} = frac{8+ sqrt{24} }{4} = frac{8+2 sqrt{6} }{4} = frac{4+ sqrt{6} }{2} \ x_{2} = frac{8- sqrt{24} }{4}= frac{8-2 sqrt{6} }{4}= frac{4- sqrt{6} }{2}$