how many solutions to this equation:
sqrt(x+7)=x*sqrt(x+7)

• Ans is 3
  sqrt(x+7)=x*sqrt(x=7)
  by squaring both sides
  x+7=x^2(x+7)
  x^3+7x^2-x-7=0
  which has three roots -1,1,-7
• 8 years agoHelpfull: Yes(16) No(10)
• sorry its 2
  sqrt(x+7)=x*sqrt(x+7)
  on cancelling sqrt(x+7) i.e. x=1
  and sqrt(x+7) can be 0 also, therefore x+7=0 hence x=-7
  therefore x=1,x=-7
• 8 years agoHelpfull: Yes(14) No(7)
• @richa
  putting -1 in the initial equation it does not satisfy so -1 is not a solution.
• 8 years agoHelpfull: Yes(10) No(0)
• in mathematics...its always suggested to not to change the degree of an equation since it may results in unnecessary roots termed as EXTRANEOUS ROOTS"...fr example if we have an simple equation say x=5 then it has only one root ie 5 (most obvious) ...however if we make square of both sides then it will be like x^2=25 and now it will have two roots x=+5 and x=-5 which is infact not appropriate with the basic equation x=5......so the buddies here who have answered it as 3 roots is not correct...it will have only 2 roots...-7 and 1
• 8 years agoHelpfull: Yes(8) No(0)
• sqrt(x+7)=x*sqrt(x+7)
  squaring both sides
  (x+7)=x^2 (x+7)
  not takin x+7 to other side
  x^2 (x+7)-(x+7)=0
  now takin x+7 common
  (x+7)(x^2 -1)=0
  this means
  either x+7=0
  or
  x^2 -1=0
  or both
  so if x+7=0
  x=-7
  if x^2-1=0
  x^2=1
  x=+1 or -1
  so x has three soln
  x=1,-1,-7
• 8 years agoHelpfull: Yes(7) No(5)
• ANS : 2
  
  if we simplify the the equation, we will get :
  (x+7) = x^2 * (x+7)
  or, x^2 = 1
  so, X = 1 and -1.
  
  The number of solution is 2
• 8 years agoHelpfull: Yes(3) No(3)
• Since solution is unique the no.of solution should be 1 but the no.of roots is 3
• 8 years agoHelpfull: Yes(3) No(1)
• ans is 2
  sqrt(x+7)=x*sqrt(x+7) ..................equ..1
  by squaring both side
  x+7=x^2(x+7)
  x^2(x+7)-(x+7)=0
  take common x+7
  (x+7)(x^2-1)=0
  (x+7)(x-1)(x+1)=0
  so we get
  x=7,x=1,x=-1
  this value put in equation (1)
  x=-1 not satisfying the equation
  hence only two solution of this equation.
• 8 years agoHelpfull: Yes(3) No(1)
• i think its 1
• 8 years agoHelpfull: Yes(1) No(3)
• after getting roots we should satisfy them in original equation as roots were obtained by modifying the equation. hence only 1,-7 are valid answers , -1 is NOT.
• 8 years agoHelpfull: Yes(1) No(1)
• i think it has only 1 solution for any value of x sqrts get cancel finally in the equation we get x=1 so only i solution
  rectify me if iam wrong
• 8 years agoHelpfull: Yes(1) No(0)
• Its Always 1 Because here only one Variable ie.X So May be x have different different Value but Solution is only 1.
• 6 years agoHelpfull: Yes(1) No(0)
• how? @garima
• 8 years agoHelpfull: Yes(0) No(1)
• 1, x=1, x=sqrt(x+7)/sqrt(x+7)
• 8 years agoHelpfull: Yes(0) No(1)
• since the above equation is a quadratic equation so the number of solutions will be three.
• 7 years agoHelpfull: Yes(0) No(0)
• there are only two solutions x= 1 and x= -7 since x=-1 doesnt satisfy the original equation
• 7 years agoHelpfull: Yes(0) No(0)
• 3....This equation will be in power of 3
• 7 years agoHelpfull: Yes(0) No(0)
• The degrees should never be altered in such type of questions because you land up with n number of solutions because you can alter/keep increasing the degree of equation n times.So
  The highest degree in the equation is 1 therefore only one solution possible.
• 4 years agoHelpfull: Yes(0) No(0)