Question

product of numbers is 224 and the sum of their square is 452. What are the numbers​

Answer 1

Answer:

Hi army This is the answer

Step-by-step explanation:

Hope it help please mark brainlist.

Answer 2

Answer:

Numbers are 14 and 16.

Step-by-step explanation:

Numerous issues can be expressed as equations and include relationships between known and unknown numbers. We refer to these issues as word problems since the equations are typically expressed in words.

• How to solve a word issue involving a linear equation:
• Carefully read the problem and make note of what is requested, what is given, and what is supplied.
• Indicate the unknown using the variables x, y, and so on.
• Convert the issue into mathematical terms or mathematical statements.
• Utilizing the conditions provided in the problems, form the linear equation in one variable.
• For the unknown, solve the equation.
• Check to make sure the solution fits the problem's requirements.

Let the two numbers be $x$ and $y.$

Product of numbers $=224$

$xy=224$...…..(1)

Sum of their square $=452$

$x^{2} +y^{2} =452$...…(2)

Add and subtract 2xy in equation (2)

$x^{2} +y^{2}+2xy-2xy =452\\(x-y)^{2} +2xy=452\\(x-y)^{2}+2(224)=452\\(x-y)^{2}+448=452\\(x+y)^{2}=452-448\\(x+y)^{2}=4$

$(x-y)=2$......(3)

Substitute $y=\frac{224}{x}$  in equation (3)

$(x-\frac{224}{x} )=2\\x^{2} -224=2x\\x^{2} -2x-224=0\\x^{2} -14x+16x-224=0\\x(x-14)+16(x-14)=0\\(x+16)(x-14)=0$

So, $x=14$ and $x=16$

#SPJ2