解答
8(x−5)7=(x−5)10
解答
x=5,x=7,x=4+3i,x=4−3i
求解步骤
8(x−5)7=(x−5)10
展开 8(x−5)7:8x7−280x6+4200x5−35000x4+175000x3−525000x2+875000x−625000
展开 (x−5)10:x10−50x9+1125x8−15000x7+131250x6−787500x5+3281250x4−9375000x3+17578125x2−19531250x+9765625
8x7−280x6+4200x5−35000x4+175000x3−525000x2+875000x−625000=x10−50x9+1125x8−15000x7+131250x6−787500x5+3281250x4−9375000x3+17578125x2−19531250x+9765625
交换两边x10−50x9+1125x8−15000x7+131250x6−787500x5+3281250x4−9375000x3+17578125x2−19531250x+9765625=8x7−280x6+4200x5−35000x4+175000x3−525000x2+875000x−625000
两边减去 8x7−280x6+4200x5−35000x4+175000x3−525000x2+875000x−625000x10−50x9+1125x8−15000x7+131250x6−787500x5+3281250x4−9375000x3+17578125x2−19531250x+9765625−(8x7−280x6+4200x5−35000x4+175000x3−525000x2+875000x−625000)=8x7−280x6+4200x5−35000x4+175000x3−525000x2+875000x−625000−(8x7−280x6+4200x5−35000x4+175000x3−525000x2+875000x−625000)
化简
x10−50x9+1125x8−15008x7+131530x6−791700x5+3316250x4−9550000x3+18103125x2−20406250x+10390625=0
因式分解 x10−50x9+1125x8−15008x7+131530x6−791700x5+3316250x4−9550000x3+18103125x2−20406250x+10390625:(x−5)7(x−7)(x2−8x+19)
(x−5)7(x−7)(x2−8x+19)=0
使用零因数法则： If ab=0then a=0or b=0x−5=0orx−7=0orx2−8x+19=0
解 x−5=0:x=5
解 x−7=0:x=7
解 x2−8x+19=0:x=4+3i,x=4−3i
解为x=5,x=7,x=4+3i,x=4−3i