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3 months ago

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

Mathematics

1 answer:

Zina [12.3K]3 months ago

7 0

Given parameters:

Equation:

(x-4)²=9

Problem: Solve the equation by both factoring and extracting the square root.

Solution:

Starting equation:

(x-4)²=9

Subtracting 9 from both sides brings us to zero;

(x-4)² - 9 = 0

(x -4)² - 3² = 0

This fits the concept of the difference of squares;

x² - y² = (x + y)(x-y)

Let x = x-4 and y = -3

Then input and solve;

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

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

S thus,

x - 7 = 0 or x-1 = 0

x = 7 or 1

<pBy extracting the square roots;

(x-4)² = 9

√(x-4)² = √9

x - 4 = 3

x = 4 + 3 = 7; however, this is not the sole solution

Thus, direct extraction of the square root is not the method for complete solutions.

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

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