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Question

Solve: axa+bxb=2cxc

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Solution

axa+bxb=2cxc
a(xb)+b(xa)(xa)(xb)=2cxc
a(xb)(xc)+b(xa)(xc)=2c(xa)(xb)
a(x2cxbx+bc)+b(x2cxax+ac)=2c(x2bxax+ab)
ax2acxabx+abc+bx2bcxabx+abc
2cx22bcx2acx+2abx
ax2+bx22cx2+acx2abx+bcx+2abc=2bcx+2abc
(a+b2c)x2+acx+bcx2abx=0
x((a+b2c)x+(ac+bc2ab))=0
x=0, (a+b2c)x+(ac+bc2ab)=0
x=0, x=2abacbca+b2c.

1110254_1208847_ans_a67a629a0c844849bd3c35f028a8656d.jpg

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