Ask a mathematical equation: X & # 179; - 2 √ 2x & # 178; + 2x - &# 141; √ 2-1 = 0 I haven't studied the cubic equation of one variable. It's a problem in the eighth grade mathematics 1. Replace √ 2 with y to make the original equation XY & # 178; - (2x & # 178; + 1) y + (X & # 179; + 1) = 0 (1) Solving the equation about y (2) From the expression of the root of the equation about y in one, and then replace y with √ 2, we get the equation about X, and then solve the two equations (3) Write the roots of the original equation (i.e. the above two roots of the X equation) Not many points, satisfied with the answer to add 50~ Please help me a lot~

Ask a mathematical equation: X & # 179; - 2 √ 2x & # 178; + 2x - &# 141; √ 2-1 = 0 I haven't studied the cubic equation of one variable. It's a problem in the eighth grade mathematics 1. Replace √ 2 with y to make the original equation XY & # 178; - (2x & # 178; + 1) y + (X & # 179; + 1) = 0 (1) Solving the equation about y (2) From the expression of the root of the equation about y in one, and then replace y with √ 2, we get the equation about X, and then solve the two equations (3) Write the roots of the original equation (i.e. the above two roots of the X equation) Not many points, satisfied with the answer to add 50~ Please help me a lot~

Triangle = 4x ^ 4 + 4x & # 178; + 1-4x ^ 4-4x = 4x & # 178; - 4x + 1 = (2x-1) & # 178;
So y = [(2x & # 178; + 1) ± (2x-1)] / 2x = √ 2
2x²+1+2x-1=2√2x
x²+(1-√2)x=0
x=0x=-1-√2
2x²+1-2x+1=2√2x
x²+(√2-1)x+1=0
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