Answer:
The value of the greater number is 30.
Step-by-step explanation:
We need to find the values of x that satisfy the equation :
[tex]x(x-5)=750[/tex]
Working with the equation ⇒
[tex]x(x-5)=750[/tex]
[tex]x^{2}-5x=750[/tex]
[tex]x^{2}-5x-750=0[/tex]
Given an equation with the form
[tex]ax^{2}+bx+c=0[/tex]
We can use the quadratic equation to find the values of x
[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex] and
[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
With [tex]a=1\\b=-5\\c=-750[/tex] we replace in the equations of x1 and x2 ⇒
[tex]x1=\frac{-(-5)+\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=30[/tex]
[tex]x1=30[/tex] is a solution of the equation [tex]x^{2}-5x-750=0[/tex]
Now for x2 ⇒
[tex]x2=\frac{-(-5)-\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=-25[/tex]
[tex]x2=-25[/tex] is a solution of the equation [tex]x^{2}-5x-750=0[/tex]
Given that both numbers are positive ⇒
[tex]x>0[/tex] and [tex](x-5)>0\\x>5[/tex]
Therefore, x2 is not a possible value for the greater number
The greater number is [tex]x1=30[/tex]
