Question

Умоляю, срочно,пожалуйста!

Answer 1

$1)2x^{2}-4sqrt{2}x+3=0\\D=(-4sqrt{2} )^{2}-4*2*3=32-24=8=(2sqrt{2} )^{2} \\x_{1}=frac{4sqrt{2}+2sqrt{2} }{4}=frac{6sqrt{2} }{4}=frac{3sqrt{2} }{2} \\x_{2}=frac{4sqrt{2} -2sqrt{2} }{4}=frac{2sqrt{2} }{4}=frac{sqrt{2} }{2}$

$2)x^{2} -x(sqrt{7}-2)-2sqrt{7}=0\\D=(sqrt{7}-2)^{2}-4*(-2sqrt{7})=7-4sqrt{7}+4+8sqrt{7}=11+4sqrt{7}=(sqrt{7}+2)^{2}\\x_{1} =frac{sqrt{7}-2+sqrt{7}+2}{2}=frac{2sqrt{7} }{2}=sqrt{7}\\x_{2}=frac{sqrt{7}-2-sqrt{7}-2}{2} =frac{-4}{2}=-2$

$3)2x^{2} -4x-17=0\\D=(-4)^{2} -4*2*(-17)=16+136=152=(2sqrt{38})^{2} \\x_{1}=frac{4+2sqrt{38} }{4}=frac{2+sqrt{38} }{2}\\x_{2}=frac{4-2sqrt{38} }{4} =frac{2-sqrt{38} }{2}$