Answer:
The numbers are
and ![-4+2\sqrt{6}](https://tex.z-dn.net/?f=-4%2B2%5Csqrt%7B6%7D)
Step-by-step explanation:
Let
x ------> one number
(x-8) ------> the another number
we know that
![x^{2} +(x-8)^{2}=80](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%28x-8%29%5E%7B2%7D%3D80)
![x^{2} +x^{2}-16x+64=80](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2Bx%5E%7B2%7D-16x%2B64%3D80)
![2x^{2}-16x+64-80=0](https://tex.z-dn.net/?f=2x%5E%7B2%7D-16x%2B64-80%3D0)
![2x^{2}-16x-16=0](https://tex.z-dn.net/?f=2x%5E%7B2%7D-16x-16%3D0)
Simplify
![x^{2}-8x-8=0](https://tex.z-dn.net/?f=x%5E%7B2%7D-8x-8%3D0)
The formula to solve a quadratic equation of the form
is equal to
![x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%28%2B%2F-%29%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%20%7B2a%7D)
in this problem we have
so
![a=1\\b=-8\\c=-8](https://tex.z-dn.net/?f=a%3D1%5C%5Cb%3D-8%5C%5Cc%3D-8)
substitute in the formula
![x=\frac{8(+/-)\sqrt{-8^{2}-4(1)(-8)}} {2(1)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B8%28%2B%2F-%29%5Csqrt%7B-8%5E%7B2%7D-4%281%29%28-8%29%7D%7D%20%7B2%281%29%7D)
![x=\frac{8(+/-)\sqrt{96}} {2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B8%28%2B%2F-%29%5Csqrt%7B96%7D%7D%20%7B2%7D)
![x=\frac{8(+/-)4\sqrt{6}} {2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B8%28%2B%2F-%294%5Csqrt%7B6%7D%7D%20%7B2%7D)
![x=4(+/-)2\sqrt{6}](https://tex.z-dn.net/?f=x%3D4%28%2B%2F-%292%5Csqrt%7B6%7D)
![x1=4(+)2\sqrt{6}](https://tex.z-dn.net/?f=x1%3D4%28%2B%292%5Csqrt%7B6%7D)
![x2=4(-)2\sqrt{6}](https://tex.z-dn.net/?f=x2%3D4%28-%292%5Csqrt%7B6%7D)
so
the solution must be a positive real number
![x=4(+)2\sqrt{6}](https://tex.z-dn.net/?f=x%3D4%28%2B%292%5Csqrt%7B6%7D)
------> ![x-8=-4(+)2\sqrt{6}](https://tex.z-dn.net/?f=x-8%3D-4%28%2B%292%5Csqrt%7B6%7D)
Shdjrdikskisjdjdjjdjdjjdjdjjdksjsjjsididiidisiieidiididiidiiieieieieieieiieieieiieiieidieiiei
Answer:
Amanda has 20, Rob has 45
Step-by-step explanation:
Amanda has ten fewer rocks than Andrew, 30-10=20
Rob has 15 more rocks than Andrew, 30+15=45
Answer:
12
Step-by-step explanation:
<h2>
The all roots are equation are 1, - 1 and - 2.</h2>
Step-by-step explanation:
The given cubic polynomial:
k(x) =
+ 2
- x -2
To find, the all roots are
+ 2
- x -2 = ?
∴ k(x) =
+ 2
- x -2
⇒
+ 2
- x -2 = 0
⇒
(x + 2) - 1(x + 2) = 0
⇒ (
- 1)(x + 2) = 0
⇒
- 1 = 0 and x + 2 = 0
⇒
- 1 = 0
⇒
= 1
⇒ x = ± 1 = 1, - 1
or, x + 2 = 0
⇒ x = - 2
Thus, the all roots are equation are 1, - 1 and - 2.