Verified answer

(3y + 1) (3y + 1) - (3y - 4)² = 7

По формуле (a - b)² = a² - 2ab + b²:

(3y + 1)² - ((3y)² - 2 · 3y · 4 + 4²) = 7

По формуле (a + b)² = a² + 2ab + b²:

(3y)² + 2 · 3y · 1 + 1² - (9y² - 24y + 16) = 7

9y² + 6y + 1 - 9y² + 24y - 16 = 7

30y - 15 = 7

30y = 7 + 15

30y = 22

y = 22/30 (сокращаем дробь на 2)

y = 11/15

Ответ: y = 11/15.

[tex](3y + 1) ^{2} - (9 {y}^{2} - 24y + 16) = 7[/tex]

[tex]9 {y}^{2} + 6y + 1 - 9 {y}^{2} + 24y - 16 = 7[/tex]

[tex]30y - 15 = 7[/tex]

[tex]30y = 7 + 15[/tex]

[tex]30y = 22[/tex]

[tex]y = \frac{11}{15} [/tex]