Question

Which of the following are solutions to the equation below x^2-8x+16=5

Answer 1

Answer:

         x₁ = 4 - √5  ;  x₂ = 4 + √5

Step-by-step explanation:

$x^2-8x+16=5\\\\x^2-8x+11=0\\\\a=1\,,\ \ b=-8\,,\ \ c=11\\\\x_1=\dfrac{-(-8)-\sqrt{(-8)^2-4\cdot1\cdot11}}{2\cdot1}=\dfrac{8-\sqrt{20}}2=\dfrac{8-2\sqrt5}2=\dfrac{2(4-\sqrt5)}2=\\\\=4-\sqrt5\\\\x_2=\dfrac{-(-8)-\sqrt{(-8)^2-4\cdot1\cdot11}}{2\cdot1}=\dfrac{8+2\sqrt5}2=4+\sqrt5$