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)

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

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)

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

4)

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

5)

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

нет корней