Question

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

Answer 1

x₁ = 4 - √5 ; x₂ = 4 + √5

Explanation:

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