Question

One number is equal to the square of another. Find the numbers if both are positive and their sum is 2450.

Answer 1

Step-by-step explanation

Step 1

set the equations

a)

let x represents the first number

let y represents the second number

so

b) translate:

One number is equal to the square of another, hence

`x=y^2\Rightarrow equation(1)`

both are positive and their sum is 2450

`x+y=2450\Rightarrow equation(2)`

Step 2

solve the equations,

a) replace the x value from equation (1) into equation (2)

`\begin{gathered} x+y=2450\Rightarrow equation(2) \\ replace \\ y^2+y=2450 \\ subtract\text{ 2450 in both sides } \\ y^2+y-2450=2450-2450 \\ y^2+y-2450=0\Rightarrow equation(3) \end{gathered}`

b) now, need to solve the quadratic equation, to do that, we can use the quadratic formula

rememeber:

`\begin{gathered} for \\ ax^2+bx+c=0 \\ t\text{he solution for x is } \\ x=(-b\pm√(b^2-4ac))/(2a) \end{gathered}`

hence