Question

Rezolvați în R ecuațiile: m) (x-7)^2=(x-7) (x+7); n) (√3x-2) (√3x+2); o) (x-5 pe 4) (3x+7)^2=0; p)0,(1)x^2-0,25=(x pe3-1 pe 2)^2.

Answer 1

m) (x-7)²=(x-7)(x+7)
x²-2·7x+7²=x²-7²
x²-14x-x²+49=-49
-14x=-49-49
x=-98/-14=7
;
n) (√3x-2) (√3x+2)=3x•(x-5)
(√3x)²-2²=3x²-15x
3x²-4=3x²-15x → 3x²-3x²+15x=4 → 15x=4 →x=4/15 ;
o) (x-5/4) (3x+7)²=0
x-5/4=0→ x=5/4
(3x+7)²=0
3x+7=0→ 3x=-7→ x=-7/3
p)0,(1)x²-0,25=(x/3-1/2)²
1/9 ·x²-25/100=x²/9-x/3+1/4
x²/9-1/4=x²/9-x/3+1/4
x²/9-x²/9+x/3=1/4+1/4
x/3=2/4
x/3=1/2→x=3/2