Решите уравнения: 1) (2x-5)2-(2x-3)(2x+3)=0; 2) (3x+5)(3x--1)2=10; 3)2(2x+1)2-8(x+1)(x-1)=34

Question

Алгебра: Решите уравнения: 1) (2x-5)2-(2x-3)(2x+3)=0; 2) (3x+5)(3x--1)2=10; 3)2(2x+1)2-8(x+1)(x-1)=34

fox370 · Accepted Answer

1) ac2-ad+c3-cd-bc2+bd= = (ac2 – ad) + (c3 –

bc2) + (bd – cd) = a·(c2 – d) + c2·(c – b) + d·(b – c) = a·(c2 – d) +

c2·(c – b) – d·(c – b) = a·(c2 – d) + c2·(c – b) – d·(c – b) = a·(c2 –

d) + (c – b)·(c2 – d) = (c2 – d)·(a + c – b)

2) mx2+my2-nx2-ny2+n-m= x2 ( m - n ) + y2 ( m - n ) - ( m - n ) = ( m-n ) (x2 + y2 - 1 )

3) am2+cm2-an+an2-cn+cn2= m2 (a + c ) + n2 ( a + c ) - n ( a + c ) = ( a+ c) ( m2 + n2 - n)

4) xy2-ny2-mx+mn+m2x-m2n= y2 ( x - n ) + m2 ( x - n) - m ( x - n ) = ( x-n) ( y2 + m2 - m )

5) a2b+a+ab2+b+2ab+2=ab ( a + b + 2 ) + ( a+ b+ 2 ) = 2 ( a+ b + 2 )

6) x2-xy+x-xy2+y3-y2= x ( x – y + 1) – y 2 ( x – y + 1)=( x – y + 1)( x – y 2 ).