Question

Sa se rezolve ecuațiile :
a) (x-4)²+(x-5)(x+5)=2(x+2)²+24
b)
(x+1)²+2(x-3)(x+3)=3(x-4)²+13
c)
(x+2)²+2(x-5)(x+5)=3(x-1)²+1

Answer 1

a) 
(x-4)²+(x-5)(x+5)=2(x+2)²+24
=>x²-8x+16+x²-25=2(x²+4x+4)+24
=>2x²-8x-9=2x²+8x+8+24
=>2x²-8x-2x²-8x=8+24+9
=>-16x=41
=>x=-41/16

b)
(x+1)²+2(x-3)(x+3)=3(x-4)²+13
=>x²+2x+1+2*(x²-9)=3*(x²-8x+16)+13
=>x²+2x+1+2x²-18=3x²-24x+48+13
=>3x²+2x-3x²+24x=48+13-1+18
=>26x=78
=>x=78/26
=>x=3

c)
(x+2)²+2(x-5)(x+5)=3(x-1)²+1
=>x²+4x+4+2(x²-25)=3(x²-2x+1)+1
=>x²+4x+4+2x²-50=3x²-6x+3+1
=>3x²+4x-3x²+6x=3+1-4+50
=>10x=50
=>x=50/10
=>x=5