Question

Знайти корені квадратного рівняння: а). 2х2 +7х –9=0; б). (5+3y)(5 –3y) = 7y – 11y2 +19

Answer 1

$2 {x}^{2} + 7x - 9 = 0 \\ d = 7 {}^{2} - 4 \times 2 \times ( - 9) = \\ 49 + 72 = 121 \\ x _{1} = \frac{ - 7 + 11}{2 \times 2} = \frac{4}{4} = 1 \\ x _{2} = \frac{ - 7 - 11}{2 \times 2} = - \frac{18}{4} = \\ - \frac{9}{2} = - 4 \frac{1}{2} = - 4.5$

$(5 + 3y)(5 - 3y) = 7y - 11y {}^{2} + 19 \\ 25 - 9 {y}^{2} = 7y - 11 {y}^{2} + 19 \\ 25 - 9 {y}^{2} - 7y + 11y {}^{2} - 19 = 0 \\ 2 {y}^{2} - 7y + 6 = 0 \\ d = ( - 7) {}^{2} - 4 \times 2 \times 6 = 49 - 48 = 1 \\ x _{1} = \frac{7 - 1}{2 \times 2} = \frac{6}{4} = \frac{3}{2} = 1.5 \\ x _{2} = \frac{7 + 1}{2 \times 2} = \frac{8}{4} = 2$

Answer 2

Объяснение:

2х² + 7х - 9 = 0

Д = 7² - 4 * 2 * (-9) = 49 + 72 = 121

√Д = √121 = 11

х1 = (-7-11)/(2*2) = -18/4 = -4,5

х2 = (-7+11)/(2*2) = 4/4 = 1

(5 + 3у)(5 - 3у) = 7у - 11у² + 19

25 - 15у + 15у - 9у² = 7у - 11у² + 19

25 - 9у² = 7у - 11у² + 19

-9у² + 11у² - 7у - 19 + 25 = 0

2у² - 7у + 6 = 0

Д = (-7)² - 4 * 2 * 6 = 49 - 48 = 1

√Д = √1 = 1

х1 = (7-1)/(2*2) = 6/4 = 1,5

х2 = (7+1)/(2*2) = 8/4 = 2