do you agree that the equation (x-4)²=9 can be solved both by factoring and extracting square roots?

The solutions by checking are incorrect for the second solution, hence the expression cannot be solved by extracting the square root. The equation can only be solved by factoring

Given the expression;

(x-4)²=9

This expression can be solved by factoring

Factoring the expression on the left hand side

(x-4)(x-4)=9

x²-4x-4x+16 = 9

x² - 8x + 16 - 9 = 0

x² - 8x + 7 = 0

x² -x - 7x + 7 = 0

x(x-1) -7(x-1) = 0

x-7 = 0 and x - 1 = 0

x = 7 and 1

This shows that the expression can be solved by factoring

The other way is by squaring both sides

(√x-4)² = ±√9

x - 4 =±√9

x = -9+4 and x = 9 + 4

x = -5 and 13

Since the solutions by checking are incorrect for the second solution, hence the expression cannot be solved by extracting the square root

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Given parameters:

  Equation:

          (x-4)²=9

Problem, solve the equation by factoring and extracting the root

Solution:

    Given equation:

                  (x-4)²=9

         subtract 9 from both sides to equate to zero;

                (x-4)² - 9 = 0

                (x -4)² - 3² = 0

  Now, this is similar to the concept of difference of two squares;

          x² - y² = (x + y)(x-y)

Here x  = x-4 and y = -3

  So input and solve;

              (x - 4 -3)(x - 4 -(-3)) = 0

              (x - 7)(x - 4+3) = 0

              (x -7)(x -1) = 0

S0,

             x - 7 = 0 or x-1 = 0

             x = 7 or 1

If we extract the square roots;

          (x-4)² = 9

         √(x-4)² = √9

              x - 4 = 3

              x  = 4 + 3 = 7; this is not the only solution to the problem

So we cannot solve it by extracting the square root.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.