How do you simplify #sqrt(m+3) - sqrt (m-1) = 1#?

2 Answers
Alan P.
Mar 26, 2017

#color(green)(m=13/4)#

Explanation:

Given #sqrt(m+3)-sqrt(m-1)=1#

separating the roots:
#rarr color(white)("XX")sqrt(m+3)=sqrt(m-1)+1#

squaring both sides
#rarr color(white)("XX")m+3=(m-1) + 2sqrt(m-1) +1#

combining the #(-1)# and #+1#, and subtracting #m# from both sides
#rarr color(white)("XX")3=2sqrt(m-1)#

reversing the sides and dividing both sides by 2
#rarr color(white)("XX")sqrt(m-1)=3/2#

squaring both sides
#rarr color(white)("XX")m-1=9/4#

adding #1(=4/4)# to both sides
#rarr color(white)("XX")m=13/4#

Barney V.
Mar 26, 2017

#m=3 1/4#

Explanation:

#sqrt(m+3)-sqrt(m-1)=1#

#:.sqrt(m+3)=sqrt(m-1)+1#

square L.H.S.and R.H.S.

#:.(sqrt(m+3))^2=(sqrt(m-1)+1)^2#

#sqrta xx sqrta=a#

#:.m+3=(m-1)+2sqrt(m-1)+1#

#:.m+3=mcancel(-1)+2sqrt(m-1)cancel(+1)#

#:.m+3=m+2sqrt(m-1)#

#:.3=cancelmcancel(-m)+2sqrt(m-1)#

#:.3=2sqrt(m-1)#

#:.2sqrt(m-1)=3#

#:.sqrt(m-1)=3/2#

square L.H.S.and R.H.S.

#:.(sqrt(m-1))^2=(3/2)^2#

#:.m-1=9/4#

#:.m=1+9/4#

#:.m=13/4#

#:.m=3 1/4#

check:

#:.sqrt(3.25+3)-sqrt(3.25-1)=1#

#:.sqrt6.25-sqrt2.25=1#

#:.2.5-1.5=1#

#:.1=1#

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