Question

(x-3)² - (x-8)² = (x√2 +1)²-2x²+10x

Answer 1

$\displaystyle (x-3)^2-(x-8)^2=(x \sqrt{2} +1)^2-2x^2+10x \\ x^2-6x+9-x^2+16x-64=2x^2+2x \sqrt{2} +1-2x^2+10x \\ x^2-6x-x^2+16x-2x^2-2x \sqrt{2} +2x^2-10x=1-9+64 \\ -2x \sqrt{2} =56 \\ x= -\frac{56}{2 \sqrt{2} } \\ x=- \frac{56 \sqrt{2} }{4} \\ \boxed{x=-14 \sqrt{2} }$