Question

3-(x-5)^2=1

(3-×)(3+×)-6=2

5-(×-2)(×+2)=3

×^2-2×+1=7

Answer 1

a)3-(x²-10x+25)=1
3-x²+10x-25-1=0
-x²+10x-23=0
x²-10x+23=0
Δ=100-92
Δ=8 =>√Δ=2√2
x₁=(10-2√2)/2=5-√2
x₂=(10+2√2)/2=5+√2

b)9-x²-6-2=0
-x²+1=0
x²-1=0
x₁=1
x₂=-1

c)5-(x²-4)-3=0
5-x²+4-1=0
-x²+8=0
x²-8=0
x²=8
x₁=2√2
x₂=-2√2

d)x²-2x+1-7=0
x²-2x-6=0
Δ=4+24
Δ=28 =>√Δ=2√7
x₁=(2-2√7)/2=1-√7
x₂=(2+2√7)/2=1+√7