Answer:
let the two number be x and y.
Given: the product of two numbers is 450.
then:
......[1]
Also from the given condition that; the first number is half the second number. Also, x>y.
i.e, ![y=\frac{1}{2}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx)
Substitute this in equation [1];
![x \times \frac{1}{2}x =450](https://tex.z-dn.net/?f=x%20%5Ctimes%20%5Cfrac%7B1%7D%7B2%7Dx%20%3D450)
or
[∴
]
Multiply both sides by 2; we get
or
or
![x=\sqrt{900} =30](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B900%7D%20%3D30)
Now, substitute this x value in [1], to solve for y;
![30 \times y=450](https://tex.z-dn.net/?f=30%20%5Ctimes%20y%3D450)
Divide by 30 from both the sides, we get;
![y = \frac{450}{30}=15](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B450%7D%7B30%7D%3D15)
Therefore, the equation
which can be used to find the value of x.
The greater number is x = 30.