Answer:
[tex]\left \{ 2,\frac{5}{4} \right \}[/tex]
Step-by-step explanation:
We know that for equation of type [tex](x-a)(x-b)=0[/tex], solutions are [tex]x=a\,,\,x=b[/tex] as both points x = a and x = b satisfy the equation (x-a)(x-b)=0
Given : equation (2x−4)(4x−5)=0
To find : Solution set of this equation .
Solution :
On dividing this equation by 2 and 4, we get
[tex]\left ( \frac{2x-4}{2} \right )\left ( \frac{4x-5}{4} \right )=0\\\left ( x-2 \right )\left ( x-\frac{5}{4} \right )=0[/tex]
On comparing equation [tex]\left ( x-2 \right )\left ( x-\frac{5}{4} \right )=0[/tex] with [tex]\left ( x-a \right )\left ( x-b \right )=0[/tex], we get [tex]a=2\,,\,b=\frac{5}{4}[/tex]
Therefore, solution set is [tex]\left \{ 2,\frac{5}{4} \right \}[/tex]
