Giải phương trình 1/x^2+5x+6 + 1/x^2+7x+12 + 1/x^2+9x+20 + 1/x^2+11x+30 =1/8

Đáp án: –10; 2

Giải thích các bước giải:

`1/(x^2+5x+6) + 1/(x^2+7x+12) + 1/(x^2+9x+20) + 1/(x^2+11x+30) = 1/8`$\\$`<=>1/(x^2+2x+3x+6) + 1/(x^2+3x+4x+12) + 1/(x^2+4x+5x+20) + 1/(x^2+5x+6x+30) = 1/8`$\\$`<=>1/((x^2+2x)+(3x+6)) + 1/((x^2+3x)+(4x+12)) + 1/((x^2+4x)+(5x+20)) + 1/((x^2+5x)+(6x+30)) = 1/8`$\\$`<=>1/(x(x+2)+3(x+2)) + 1/(x(x+3)+4(x+3)) + 1/(x(x+4)+5(x+4)) + 1/(x(x+5)+6(x+5)) = 1/8`$\\$`<=>1/((x+2)(x+3)) + 1/((x+3)(x+4)) + 1/((x+4)(x+5)) + 1/((x+5)(x+6)) = 1/8` $\\$ ĐKXĐ: `x\ne`$-2;-3;-4;-5;-6$$\\$` <=>1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)+1/(x+5)-1/(x+6)=1/8`$\\$`<=>1/(x+2)-1/(x+6)=1/8`$\\$`<=>((x+6))/((x+2)(x+6))-((x+2))/((x+6)(x+2))=1/8`$\\$`<=>((x+6)-(x+2))/((x+2)(x+6))=1/8`$\\$`<=>(x+6-x-2)/((x+2)(x+6))=1/8`$\\$`<=>4/((x+2)(x+6))=1/8`$\\$`<=> 4.8=(x+2)(x+6)`$\\$`<=>32=x^2+6x+2x+12`$\\$`<=>32=x^2+8x+12`$\\$`<=>x^2+8x+12-32`$\\$`<=>x^2+8x-20=0`$\\$`<=>x^2+10x-2x-20=0`$\\$`<=>(x^2+10x)-(2x+20)=0`$\\$`<=>x(x+10)-2(x+10)=0`$\\$`<=>(x+10)(x-2)=0`$\\$`<=>`$\left[\begin{matrix} x+10=0\\ x-2=0\end{matrix}\right.$$\\$`<=>`\(\left[\begin{array}{I}x=-10\\x=2\end{array}\right.\)

Vậy `\text{S =}` `{`${-10;2}$`}`