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Chapter 3: Q. 40 (page 172)

Show that the inequality (x-2)2>0has one real number that is not a solution.

Short Answer

Expert verified
  • From the graph, it can be observed that the function lies on or above the horizontal axis.
  • So, the solution set of the points above the axis will exclude only the point where the graph is on the horizontal axis.

Step by step solution

01

Step 1. Given Information

The given inequality is(x-2)2>0.

02

Step 2. Find the Intercepts

  • Consider the function f(x)=(x-2)2
  • f(x)=0for x=2.
  • So, the x- intercept is (2,0).
  • The value of f(0)is 4.
  • So, the value of y-intercept is (0,4).
  • The vertex of the function is at(2,0).
03

Step 3. Plot the Function

  • Use the obtained intercepts to plot the function.

  • From the graph, it can be observed that the function lies on or above the horizontal axis.
  • So, the solution set of the points above the axis will exclude only the point where the graph is on the horizontal axis.

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