Question

уравнение √(6+2√5) ⋅x-30=x√5 . можно пожалуйста подробно.

Answer 1

√(√5+1)²*x-x√5=30
x(|√5+1|-√5)=30
x(√5+1-√5)=30
x*1=30
x=30

Answer 2

$\sqrt{6+2\sqrt{5}}(x-30)=x\sqrt{5}\\\sqrt{5+2\sqrt{5}+1}(x-30)-x\sqrt{5}=0\\\sqrt{(\sqrt{5})^2+2\sqrt{5}+1^2}(x-30)-x\sqrt{5}=0\\\sqrt{(\sqrt{5}+1)^2}(x-30)-x\sqrt{5}=0\\|\sqrt{5}+1|(x-30)-x\sqrt{5}=0\\\sqrt{5}x-30\sqrt{5}+x-30-x\sqrt{5}=0\\x=30\sqrt{5}+30$