Question

Помогите пожалуйста)

Answer 1

$1. \ b_{3} =4, b_{6} = frac{1}{2} \ q= frac{1}{2} \ b_1=16 \ S= frac{b_1}{1-q} = frac{16}{1- frac{1}{2} } =32$
$2. \ a) sqrt{32} - sqrt{50} - sqrt{18} =4 sqrt{2} -5 sqrt{2} -3 sqrt{2} =-4 sqrt{2} \ b) sqrt[3]{3 sqrt[3]{2} } = sqrt[3]{ sqrt[3]{54} } = sqrt[9]{54}$
$3. sqrt{1- x^{2} } * sqrt{x} \ left { {{x geq 0} atop {1-x^{2} geq 0}} right. \ left { {{x geq 0} atop { x^{2} leq 1}} right. \ left { {{x geq 0} atop {-1 leq x leq 1} right.$
x ∈ (0; 1)
$4. \ a) frac{ sqrt{x} - sqrt{y} }{x-y} = frac{ sqrt{x} - sqrt{y} }{( sqrt{x} - sqrt{y} )( sqrt{x} + sqrt{y} )} = frac{1}{ sqrt{x} + sqrt{y} } \ b) frac{ sqrt{x} - sqrt{y} }{ sqrt[4]{x}- sqrt[4]{y}}= frac{( sqrt[4]{x}- sqrt[4]{y}) ( sqrt[4]{x}+ sqrt[4]{y} ) }{ sqrt[4]{x}- sqrt[4]{y}} = sqrt[4]{x} + sqrt[4]{y}$