How many solutions exists for √(x+5) = x√(x+5)

a.1

b.2

c.3

d.4

• b. 2
  
  √(x+5) = x√(x+5)
  => √(x+5) - x√(x+5) = 0
  => √(x+5)*(1-x) = 0
  => (x+5) = 0 or (1-x)= 0
  => x = 1, -5
  
  if squaring is done then u will get three roots x = -1, 1, -5
  but x= -1, doesn't satisfy the given eqn
  so, two soln esist.
  
  
• 10 years agoHelpfull: Yes(48) No(3)
• c.3
  
  √(x+5) = x√(x+5)
  on squaring both sides we will get
  (x+5)=x^2(x+5)
  on rearranging the eqution,we will get
  =>x^2(x+5)-(x+5)=0
  
  =>(x+5)(x^2-1)=0
  
  =>either (x+5)=0 or (x^2-1)=0
  
  =>hence,x can be -5,1,-1
  so there will be three solutions
• 10 years agoHelpfull: Yes(12) No(11)
• ans is 2...
  √(x+5)-x√(x+5)=0
  take √(x+5) common n there will be two sol for x
• 10 years agoHelpfull: Yes(2) No(2)
• Given, sqrt(x+5) = x sqrt(x+5)
  Squaring both sides we get:
  
  (x + 5) = x^2(x + 5)
  
  => x^2(x + 5) - (x + 5) = 0
  
  => (x^2 - 1)(x + 5) = 0
  
  => x = 1, -1, -5
  
  so When x = 1:
  sqrt(x+5) = x sqrt(x+5)
  
  => sqrt(1+5) = 1 xx sqrt(1+5)
  
  => sqrt(6) = sqrt(6) (which is true)
  
  When x = -5:
  sqrt(x+5) = x sqrt(x+5)
  
  => sqrt(-5+5) = -5 xx sqrt(-5+5)
  
  => sqrt(0) = -5 * sqrt(0)
  
  => 0 = 0 (which is true)
  
  When x = -1:
  sqrt(x+5) = x sqrt(x+5)
  
  => sqrt(-1+5) = -1 xx sqrt(-1+5)
  
  => sqrt(4) = -sqrt(4)
  
  => 2 = -2 (which is not true)
  
  So for the given equation we can have two values of x.
• 7 years agoHelpfull: Yes(2) No(0)
• 2,(x+5)=x^2(x+5)=>x^2=1
• 10 years agoHelpfull: Yes(0) No(0)
• c.3
  Nobody said x can't be 0
  The solutions are x = 0,1,-5
• 10 years agoHelpfull: Yes(0) No(10)
• no of soutions will be 2
• 10 years agoHelpfull: Yes(0) No(0)
• There are three solutions but 2 satisfies the condition hence ans is 2
• 10 years agoHelpfull: Yes(0) No(0)
• c.3
  
  √(x+5) = x√(x+5)
  on squaring both sides we will get
  (x+5)=x^2(x+5)
  on rearranging the eqution,we will get
  =>x^2(x+5)-(x+5)=0
  
  =>(x+5)(x^2-1)=0
  =>(x+5)(x-1)(x+1)=0
  => 3 solutions
  
• 9 years agoHelpfull: Yes(0) No(2)
• 4 sol:arrange as per data.i get 4
• 9 years agoHelpfull: Yes(0) No(2)
• ans is 2
  on squaring both side we get
  x+5 = x^2(x+5)
  => x^2 = 1
  => x =+-1
  
• 9 years agoHelpfull: Yes(0) No(2)
• ans b
  √(x+5) = x√(x+5)
  
  take square both side
  then
  (x+5)=x^2(x+5)
  solve it we find
  x^2=1
  then
  x=1,x=-1
  we put the value of x in the equation
  and satisfy these value
  and there are solution
  
• 9 years agoHelpfull: Yes(0) No(1)