Question

answer. attempt 1 out of 2 write two numbers that multiply to the value on top and add to the value on bottom. 14 + 45 ×

Explanation:

Step1: Let the two - numbers be \(x\) and \(y\).

We have the equations \(xy = 45\) and \(x + y=14\). From \(x + y = 14\), we can express \(y = 14 - x\).

Step2: Substitute \(y = 14 - x\) into \(xy = 45\).

We get \(x(14 - x)=45\), which expands to \(14x-x^{2}=45\), or \(x^{2}-14x + 45=0\).

Step3: Factor the quadratic equation.

For the quadratic equation \(ax^{2}+bx + c = 0\) (here \(a = 1\), \(b=-14\), \(c = 45\)), we need to find two numbers that multiply to \(ac=45\) and add up to \(b=-14\). The factored form is \((x - 5)(x - 9)=0\).

Step4: Solve for \(x\).

Setting each factor equal to zero gives \(x-5 = 0\) or \(x - 9=0\). So \(x = 5\) or \(x = 9\). When \(x = 5\), \(y=14 - 5=9\); when \(x = 9\), \(y=14 - 9 = 5\).

Answer:

5 and 9