Question

(x-1)⁵+(x+3)⁵=242(x+1)

Answer 1

3) (x−1)5+(x+3)5=242(x+1)(x−1)5+(x+3)5=242(x+1)

- Đặt x+1=y⇒x−1=y−2;x+3=y+2x+1=y⇒x−1=y−2;x+3=y+2

- Ta có:

(y−2)5+(y+2)5=242y(y−2)5+(y+2)5=242y

⇔y5−5y4+40y3−80y2+80y−32+y5+5y4+40y3+80y2+80y+32=242y⇔y5−5y4+40y3−80y2+80y−32+y5+5y4+40y3+80y2+80y+32=242y

⇔2y5+80y3+160y−242y=0⇔2y5+80y3+160y−242y=0

⇔2y5+80y3−82y=0⇔2y5+80y3−82y=0

⇔2y(y4+40y2−41)=0⇔2y(y4+40y2−41)=0

⇔2y(y4+41y2−y2−41)=0⇔2y(y4+41y2−y2−41)=0

⇔2y[y2(y2+41)−(y2+41)]=0⇔2y[y2(y2+41)−(y2+41)]=0

⇔2y(y2−1)(y2+41)=0⇔2y(y2−1)(y2+41)=0

⇔2y(y−1)(y+1)(y2+41)=0⇔2y(y−1)(y+1)(y2+41)=0

⇔y=0;y−1=0⇒y=1;y+1=0⇒y=−1⇔y=0;y−1=0⇒y=1;y+1=0⇒y=−1

⇔y=0⇒x+1=0⇒x=−1⇔y=0⇒x+1=0⇒x=−1

⇔y=1⇒x+1=1⇒x=0⇔y=1⇒x+1=1⇒x=0

⇔y=−1⇒x+1=−1⇒x=−2