a times b equals -8. a plus b equals 7. what is a and b?

a times b equals -8. a plus b equals 7. what is a and b?

$$\small{ \begin{array}{lrcl} (1) & a\cdot b&=& -8\\ (2) & a+b &=& 7\\ & \mathbf{b} & \mathbf{=} & \mathbf{7-a}\\ \hline (2) \text{ in } (1) & a\cdot (7-a) &=& -8 \\ & 7a-a^2 &=& -8 \\ & a^2 - 7a -8 &=& 0\\ & (a-8)(a+1) &=& 0 \\ & \mathbf{a_1} & \mathbf{=} & \mathbf{8} \\ & \mathbf{a_2} & \mathbf{=} & \mathbf{-1} \\ \hline & b_1 &=& 7-a_1 \\ & b_1 &=& 7 - 8 \\ & \mathbf{b_1} & \mathbf{=} & \mathbf{-1} \\ & b_2 &=& 7 - a_2 \\ & b_2 &=& 7 -(-1) \\ & b_2 &=& 7+1 \\ & \mathbf{b_2} & \mathbf{=} & \mathbf{8} \end{array} }$$

$$\small{ \begin{array}{lclccl} a_1 = 8 \quad &\text{ and } \quad b_1 &=& -1\\ a_2 = -1 \quad &\text{ and } \quad b_2 &=& 8 \end{array} }$$

Hallo anonymous!

a times b equals -8. a plus b equals 7. what is a and b?

a * b = - 8

a + b = 7

a = - 8 / b

a = 7 - b

- 8 / b = 7 - b

- 8 = 7b - b²

b² - 7b - 8 = 0

b1;2 = - (p/2) ±√((p/2)² -q)

b1;2 = 3,5 ±√ (3,5² + 8)

b1;2 = 3,5 ±√ 20,25 = 3,5 ± 4,5

b1 = 8

b2 = -1

a1;2 = 7 - b

a1 = -1

a2 = 8

test :

a1 * b1 = - 8                 

-1 * 8  = - 8   okey

a1 + b1 = 7

-1 + 8 = 7      okey

a2 * b2 = - 8

8 * (- 1) = - 8 okey

a2 + b2 = 7

8 + (-1) = 7 okey

greetings   :- )