Question

1 rezolvati in R
a) (2x-3)²+(2x+3)²=(2√2x-3)(2√2x+3)+x-1;
b) (x-1)²=x²+2x=3;
c) (x+2)²+(x-3)²-2(x+2)(x-3)+5x=0;
d) x²+y²-2√5y+4√5x+25=0;
e) x√2-x√5+2√10=7;
f) (√2-1)x+2=2√2-2x(1-√2)

Answer 1

a) (2x-3)²+(2x+3)²=(2√2x-3)(2√2x+3)+x-1
4x²-12x+9+4x²+12x+9=8x²-9+x-1
8x²-8x²-x=-9-1-9-9
-x=-28    inmultim -1
x=28

b) (x-1)²=x²+2x=3;
x²-2x+1-x²-2x=3
-4x=3-1
-4x=2    ·(-1)
x=-2/4
x=-1/2

c) (x+2)²+(x-3)²-2(x+2)(x-3)+5x=0;
x²+4x+4+x²-6x+9-2(x²-3x+2x-6)+5x=0
2x²-2x+13-2x²+x+6+5x=0
4x+19=0
x=-19/4

e) x√2-x√5+2√10=7;
x(√2-√5)=7-2√10
x=(7-2√10)/(√2-√5)
x=(7-2√10)(√2+√5)/(2-5)
x=(14+7√5-2√12-2√50)/-3
x=-(14+7√5-4√3-10√2)/3

f) (√2-1)x+2=2√2-2x(1-√2)
√2x-x+2=2√2-2x+2√2x
√2x-x-2-2√2+2x-2√2x=0
-√2x+x=2+2√2
x(1-√2)=2(1+√2)
x=2(1+√2)/(1-√2)
x=2(1+√2)(1+√2)/(1-2)
x=-2(1+2√2+2)
x=-2(3+2√2)