Respuesta :
Statement 1:
Let the smaller number be x
Let the larger number be y
The difference between two whole numbers is 2 can be written as
[tex]y-x=2[/tex]Statement 2:
Two times the square of the smaller number is:
[tex]2\times x^2=2x^2[/tex]Three times the square of the larger number is:
[tex]3\times y^2=3y^2[/tex]Thus,
[tex]2x^2+3y^2=140[/tex]Therefore we would solve the system of equations to find the two numbers
[tex]\begin{gathered} From\text{ statement 1} \\ y=2+x \\ \therefore \\ 2x^2+3(2+x)^2=140 \\ 2x^2+3((x+2)(x+2))=140 \end{gathered}[/tex][tex]\begin{gathered} 2x^2+3(x^2+4x+4)=140 \\ 2x^2+3x^2+12x+12=10 \\ 5x^2+12x+12=140 \\ 5x^2+12x+12-140=0 \\ 5x^2+12x-128=0 \end{gathered}[/tex][tex]\begin{gathered} (x-4)(5x+32)=0 \\ x-4=0 \\ x=4 \\ OR \\ 5x+32=0 \\ 5x=-32 \\ x=-\frac{32}{5}=-6.4 \end{gathered}[/tex]To find y, we would use x =4, because the statement said the numbers are whole numbers
[tex]\begin{gathered} y=2+x \\ where\text{ x=4} \\ y=2+4=6 \\ \end{gathered}[/tex]Hence, the numbers are 4 and 6
