Question

(x²-7x+6)²-x²+10x-25=0

Answer 1

(x²-7x+6)²-x²+10x-25=0
(х^2-7х+6)^2=х^2-10х+25
(х^2-7х+6)^2-(х-5)^2=0 (х^2-7х+6-х+5)*(х^2-7х+6+х-5)=0 х^2-6x+1=0 D=(-(-6)^2-4*1*1=36-4=32 x1=(-(-6)-V32)/2*1=(6-V32)/2=(6-4V2)/2=(3-2V2) x2=(-(-6)+V32)/2*1=(6+V32)/2=(6+4V2)/2=(3+2V2) x^2-8x+11=0 D=(-(-8))^2-4*1*11=64-44=20 x3=(-(-8)-V20)/2*1=(8-2V5)/2=(4-V5) x4=(-(-8)+V20)/2*1=(8+2V5)/2=(4+V5)

Answer 2

(x²-7x+6)²-x²+10x-25=0
(x²-7x+6)²-(x²-10x+25)=0
(x²-7x+6)²-(x-5)²=0
используем a²-b²=(a-b)(a+b)
(x²-7x+6 - x + 5)(x²-7x+6 + x - 5)=0
(x²-8x+11)(x²-6x+1)=0
x²-8x+11=0
D=64-44=20
x₁₂=(8+-√20)/2=(8+-2√5)/2=4+-√5
x²-6x+1=0
D=36-4=32
x₃₄=(6+-√32)/2=(6+-4√2)/2=3+-2√2
ответ 4+-√5 3+-2√2