Question

(9-y)^2-y(y+1) при y= -2/19

Answer 1

$(9-y)^2-y(y+1)=\\\\=9^2-2\cdot 9\cdot y+y^2-y\cdot y-y\cdot 1=\\\\=81\ \underline{\underline{-18y}}\ \underline{+y^2}\ \underline{-y^2}\ \underline{\underline{-y}}=81-19y$

$y=-\dfrac2{19}\\\\81-19\cdot\left(-\dfrac2{19}\right)=81+\dfrac{19\cdot 2}{19}=81+2=83$

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Использована формула квадрата разности:

$(a-b)^2=a^2-2ab+b^2$

Ответ: 83

Answer 2

To evaluate the expression (9 - y)^2 - y(y + 1) when y = -2/19, we substitute the value of y into the expression and perform the necessary calculations.

Let's substitute y = -2/19 into the expression:

(9 - (-2/19))^2 - (-2/19)(-2/19 + 1)

Simplifying further:

(9 + 2/19)^2 - (-2/19)(-2/19 + 19/19)

To add fractions with different denominators, we need to find a common denominator:

(9 + 2/19)^2 - (-2/19)(17/19)

Calculating the expression within parentheses:

(171/19)^2 - (-34/19)(17/19)

Squaring 171/19:

(29241/361) - (-34/19)(17/19)

Multiplying the fractions:

(29241/361) - (-578/361)

To subtract fractions, we need a common denominator:

(29241/361) + (578/361)

Adding the fractions:

29819/361

Therefore, when y = -2/19, the value of the expression (9 - y)^2 - y(y + 1) is 29819/361.