The difference of the square of two consecutive even integers is 60.what are these number?
Answer (1)
The answer to the given word problem is 16 and 14Let's express the question into an equation. It says difference so it mean's the operation is subtraction: -The square of 2 consecutive even integer, we can express that as [tex]x^{2}[/tex] and [tex]x^{2} +2[/tex]It also says that the answer is 60, so we'll equate it to 60Thus, the final equation is [tex]x^{2} - (x+2)^2=60[/tex]To subtract this, we first square the one inside the parenthesis. We can do this by FOIL(x+2)(x+2)=x²+4x+4We put this back in the equation and it'll be:[tex]x^{2} -x^{2} +4x+4=60[/tex]Solve for like terms4x+4=60Transpose 4 to become -44x=60-44x=56Divide both sides by 4[tex]\frac{4x}{4} =\frac{56}{4}[/tex]x=14 Now we know that one term is 14, to find the other term, we substitute it to x+2x+2=14+2=16Therefore, the two numbers are 14 and 16We can check it by squaring it and subtracting.16²=25614²=196=256-196=60Therefore, the answer is correct!
