Q. How many solution exists for (x+5)^1/2=x(x+5)^1/2

Option
1)1
2)2
3)3
4)4

• (x+5)^1/2=x*(x+5)^1/2
  or (x+5)^1/2-x*(x+5)^1/2=0
  or (x+5)^1/2*(1-x)=0
  or (x+5)^1/2=0 ,1-x=0
  or x=-5 ,x=1
  only two solution
  option(2)
• 11 years agoHelpfull: Yes(48) No(1)
• (x+5)^2 = x*(x+5)^2
  => (x+5)= x^2 * (x+5)
  => x^2(x+5)-(x+5)=0
  => (x^2-1)(x+5)=0
  => x=+1,-1,-5
  But x=-1 do not satisfy the original equation so only two values are there which are x=1 and x=-5
  So answer is 2.
• 11 years agoHelpfull: Yes(13) No(5)
• Only one solution can exist i.e X=1
  so,option(1)
  
• 11 years agoHelpfull: Yes(4) No(6)
• (x+5)^1/2 = x*(x+5)^1/2
  => (x+5)= x^2 * (x+5)
  => x^2(x+5)-(x+5)=0
  => (x^2-1)(x+5)=0
  => x=+1,-1,-5
  But x=-1 do not satisfy the original equation so only two values are there which are x=1 and x=-5
  So answer is 2.
• 11 years agoHelpfull: Yes(2) No(3)
• There are two solutions for this problem
  equation satisfies for x=0 and 1
  hence option(2)
• 11 years agoHelpfull: Yes(1) No(6)
• the answer is 2 as only 1,-5 satisfies the given equation
• 11 years agoHelpfull: Yes(1) No(0)
• (x+5)^1/2=x*(x+5)^1/2
  here two solution is possibel
  1.(x+5)^1/2=x*(x+5)^1/2
  or,(x+5)=x*(x+5)
  or,x+5=x^2+5x
  or,x^2+4x-5=0
  or,(x-1)(x+5)=0
  or,x=1 and x=-5 (x+5)^1/2
  
  2.(x+5)^1/2=x*(x+5)^1/2
  or,(x+5)^1/2/(x+5)^1/2=x
  or,x=1
  
  Which one is correct??????
  
• 11 years agoHelpfull: Yes(1) No(2)
• 2 solutions -5,5
• 11 years agoHelpfull: Yes(0) No(4)
• (x+5)^2 = x*(x+5)^2
  (x+5)^2/(x+5)^2 = x
  x=1 hence ans is 1
• 11 years agoHelpfull: Yes(0) No(0)
• ans is 3
  equation satisfy for X=0,1,-5
  
• 11 years agoHelpfull: Yes(0) No(1)
• (x+5)^1/2(1-x)=0
  then from this
  1-x=0
  x=0
  and (x+5)1/2=0 is a positive number which can't be zero hence only one solution
• 11 years agoHelpfull: Yes(0) No(0)
• why x=-1 dusnt satisfy d equation??
• 11 years agoHelpfull: Yes(0) No(0)
• (x+5)^1/2(1-x)=0
  then from this
  1-x=0 then
  x=1
  and (x+5)1/2=0 is a positive number which can't be zero hence only one solution
  
• 11 years agoHelpfull: Yes(0) No(0)
• given that
  (x+5)^1/2=x(x+5)^1/2
  therefore
  (x+5)^1/2*(1-x)=0
  (x+5)^1/2=0 and 1-x=0
  hence; x=-5 and x=1.
  now option 2 is correct.
• 11 years agoHelpfull: Yes(0) No(0)
• 3 solutions
  
  (x+5)^1/2 = x*(x+5)^1/2
  
  Squaring both sides
  
  x+5 = ( x^2 ) * (x+5)
  
  x+5 = x^3 + 5x^2
  
  => x^3 + 5x^2 - x -5 = 0
  
  => x^2(x+5) -1 (x+5)=0
  
  => (x^2 - 1) ( x + 5 )=0
  
  One solution -5
  
  Now x^2-1=0
  
  (x-1)(x+1)=0
  x=-1,1
  
  So total 3 solutions 1,-1,-5
• 10 years agoHelpfull: Yes(0) No(2)
• (x+5)^1/2=x(x+5)^1/2
  oor (x+5)^1/2-x*(x+5)^1/2=0
  or (x+5)^1/2*(1-x)=0
  
• 10 years agoHelpfull: Yes(0) No(0)