Question

Решите неполные квадратные уравнения.
1) 4х²-3,3х=0
2)4х²-0,09=0
3)8х²-0,5х=0
4)-4х²+17х=0
5)81х²+64=0

Answer 1

1)

$\displaystyle \tt 4x^2-3,3x=0 \: \: \: \: | \cdot 10\\\displaystyle \tt 40x^2-33x=0\\\displaystyle \tt x(40x-33)=0\\\displaystyle \tt \bold{x_1=0}\\\displaystyle \tt 40x-33=0\\\displaystyle \tt 40x=33\\\displaystyle \tt x=33\div40\\\displaystyle \tt \bold{x_2=0,825}$

2)

$\displaystyle \tt 4x^2-0,09=0\:\:\:\: | \cdot100\\\\ \displaystyle \tt 400x^2-9=0\\\\ \displaystyle \tt 400x^2=9\\\\ \displaystyle \tt x^2=\frac{9}{400}\\\\\displaystyle \tt x=\sqrt{\frac{9}{400}}\\\\ \displaystyle \tt x=\frac{3}{20}\\\\ \displaystyle \tt \bold{x_1=0,15}\\\\ \displaystyle \tt x=-\sqrt{\frac{9}{400}}\\\\\displaystyle \tt x=-\frac{3}{20}\\\\ \displaystyle \tt \bold{x_2=-0,15}$

3)

$\displaystyle \tt 8x^2-0,5x=0\:\:\:\:|\div0,5\\\displaystyle \tt 16x^2-x=0\\\displaystyle \tt x(16x-1)=0\\\displaystyle \tt \bold{x_1=0}\\\displaystyle \tt 16x-1=0\\\displaystyle \tt 16x=1\\\displaystyle \tt x=1\div16\\\displaystyle \tt \bold{x_2=0,0625}$

4)

$\displaystyle \tt -4x^2+17x=0\\\displaystyle \tt -x(4x-17)=0\\\displaystyle \tt x(4x-17)=0\\\displaystyle \tt \bold{x_1=0}\\\displaystyle \tt 4x-17=0\\\displaystyle \tt 4x=17\\\displaystyle \tt x=17\div4\\\displaystyle \tt \bold{x_2=4,25}$

5)

$\displaystyle \tt 81x^2+64=0\\\\ \displaystyle \tt 81x^2=-64\\\\ \displaystyle \tt x^2=-\frac{64}{81}$

нет корней