Mister Exam
分解 y^2+7*y-10 平方
解答
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(y^{2} + 7 y\right) - 10$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 7$$
$$c = -10$$
Then
$$m = \frac{7}{2}$$
$$n = - \frac{89}{4}$$
So,
$$\left(y + \frac{7}{2}\right)^{2} - \frac{89}{4}$$
$$\left(y^{2} + 7 y\right) - 10$$
To do this, let's use the formula
$$a y^{2} + b y + c = a \left(m + y\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 7$$
$$c = -10$$
Then
$$m = \frac{7}{2}$$
$$n = - \frac{89}{4}$$
So,
$$\left(y + \frac{7}{2}\right)^{2} - \frac{89}{4}$$
Factorization
[src]
/ ____\ / ____\ | 7 \/ 89 | | 7 \/ 89 | |x + - - ------|*|x + - + ------| \ 2 2 / \ 2 2 /
$$\left(x + \left(\frac{7}{2} - \frac{\sqrt{89}}{2}\right)\right) \left(x + \left(\frac{7}{2} + \frac{\sqrt{89}}{2}\right)\right)$$
(x + 7/2 - sqrt(89)/2)*(x + 7/2 + sqrt(89)/2)