How do you solve #sqrt (10x+6) - sqrt (x+1) = sqrt (8x-8) #?

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Answer 1 · 2018-07-20T12:11:41

The solution is #S={3}#

The equation is

#sqrt(10x+6)-sqrt(x+1)=sqrt(8x-8)#

Squaring both sides

#(sqrt(10x+6)-sqrt(x+1))^2=(8x-8)#

#10x+6+x+1-2sqrt((10x+6)(x+1))=8x-8#

#11x+7-2sqrt((10x+6)(x+1))=8x-8#

#3x+15=2sqrt((10x+6)(x+1))#

Squaring both sides

#(3x+15)^2=4((10x+6)(x+1))#

#9x^2+90x+225=4(10x^2+16x+6)#

#9x^2+90x+225=40x^2+64x+24#

#31x^2-26x-201=0#

Solving this quadratic equation

#x=(26+-sqrt(26^2+4*31*201))/(2*31)#

#=(26+-160)/(62)#

#x_1=3#

#x_2=-2.16#

We keep only #x_1=3#