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Question

Solve for
x:1a+b+x=1a+1b+1x{a0,bx(ab)}

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Solution

Given,

1a+b+x=1a+1b+1x

abx=bx(x+a+b)+ax(x+a+b)+ab(x+a+b)

abx=bx2+abx+b2x+ax2+a2x+abx+abx+a2b+ab2

(a+b)x2+(a2+b2+2ab)x+ab2+a2b=0

x1,2=b±b24ac2a

x=(a2+b2+2ab)±(a2+b2+2ab)24(a+b)(ab2+a2b)2(a+b)

=2b(a+b)2(a+b),2a(a+b)2(a+b)

x=b,a

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