Question

3.Rezolvati in R ecuatiile :
c)x²-12x+36=3
e)x²+10x=24
g) 25x²-10x-8=0
i)5 supra x-1=x-1 supra 45
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Answer 1

c)x²-12x+36-3=0
(x-6)²-3=0
(x-6+√3)(x-6-√3)=0
x-6+√3=0, x=6-√3
x-6-√3=0, x=6+√3

e) x²+10x-24=0
x²+10x+25-49=0
(x+5)²-7²=0
(x+5-7)(x+5+7)=0
x-2=0, x=2
x+12=0, x=-12

g) 25x²-10x+1-9=0
(5x-1)²-3²=0
(5x-1+3)(5x-1-3)=0
5(x-1/5+3/5)=0,  x+2/5=0, x=- 2/5
5(x-1/5-3/5)=0, x-4/5=0, x=4/5

i) (x-1)(x-1)=45*5
(x-1)²=225
(x-1)²-15²=0
(x-1-15)(x-1+15)=0
x-16=0, x=16
x+14=0, x=-14