Solve the equation using the square root property:

\[ x^2 - 8x + 16 = 1 \]

x^2-8x+16=1\ \x^2-8x+16-1=0\ \x^2-8x+15=0\ \\Delta = b^{2}-4ac = (-8)^{2}-4 1 15=64-60=4 \ \x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{8- \sqrt{4}}{2}=\frac{8-2}{2}= \frac{6}{2}=3\ \x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{8+ \sqrt{4}}{2}=\frac{8+2}{2}= \frac{10}{2}=5\ \Answer : x=3 \ \ or \ \ x = 5

Answered by Lilith | 2024-06-10

The solutions to the equation x 2 − 8 x + 16 = 1 are x = 5 and x = 3 . This was determined by factoring the quadratic expression and using the zero product property. Both solutions can be found easily from the factored form of the equation.
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Answered by Lilith | 2024-12-23