Respuesta :
Answer :
The two numbers 21 and -14 multiply to -294 and add up to 7
Step-by-step explanation:
We have to solve the system:
a + b = 7
ab = -294
Then
b = 7 - a
a(7 - a) = -294 (substitute b by 7 - a)
Then
b = 7 - a
7a - a² = -294
Then
b = 7 - a
a² - 7a - 294 = 0
Then
b = -294 - a
a² + 294a + 7 = 0
Then
[tex]a=\frac{7+ \sqrt{7^{2}+4 \times 294} }{2} =\frac{7+ \sqrt{1225} }{2} = =\frac{7+35}{2}=\frac{42}{2} =21[/tex]
Or
[tex]a=\frac{7- \sqrt{7^{2}+4 \times 294} }{2} =\frac{7- \sqrt{1225} }{2} = =\frac{7-35}{2}=\frac{-28}{2} =-14[/tex]
Then
b = 7 - a = 7 - 21 = -14
Or
b = 7 - a = 7 - (-14) = 21
Answer: -14 and 21
Step-by-step explanation:
Let two numbers will be x and y.
Hence,
[tex]\displaystyle\\\left \{ {{x+y=7} \atop {x*y=-294}} \right.\\\\\left \{ {{y=7-x} \atop {x*(7-x)=-294}} \right. \\\\\left \{ {{y=7-x} \atop {7x-x^2=-294}} \right. \\\\\left \{ {{y=7-x} \atop {7x-x^2+x^2=-294+x^2}} \right. \\\\\left \{ {{y=7-x} \atop {7x=x^2-294}} \right. \\\\\left \{ {{y=7-x} \atop {7x-7x=x^2-294-7x}} \right. \\\\\left \{ {{y=7-x} \atop {0=x^2-7x-294}} \right. \\\\x^2-7x-294=0\\D=(-7)^2-4*1*(-294)\\D=49+1176\\D=1225\\\sqrt{D}=\sqrt{1225} \\\sqrt{D}=35\\\\[/tex]
[tex]\displaystyle\\ x=\frac{-(-7)б35}{2} \\\\x=\frac{7б35}{2} \\\\x=-14\\y=7-(-14)\\y=7+14\\y=21\\\\x=21\\y=7-21\\y=-14[/tex]
