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

2 Answers
Alan P.
Mar 26, 2017

color(green)(m=13/4)m=134

Explanation:

Given sqrt(m+3)-sqrt(m-1)=1√m+3−√m−1=1

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

squaring both sides
rarr color(white)("XX")m+3=(m-1) + 2sqrt(m-1) +1→XXm+3=(m−1)+2√m−1+1

combining the (-1)(−1) and +1+1, and subtracting mm from both sides
rarr color(white)("XX")3=2sqrt(m-1)→XX3=2√m−1

reversing the sides and dividing both sides by 2
rarr color(white)("XX")sqrt(m-1)=3/2→XX√m−1=32

squaring both sides
rarr color(white)("XX")m-1=9/4→XXm−1=94

adding 1(=4/4)1(=44) to both sides
rarr color(white)("XX")m=13/4→XXm=134

Barney V.
Mar 26, 2017

m=3 1/4m=314

Explanation:

sqrt(m+3)-sqrt(m-1)=1√m+3−√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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