in this question, x^y means x raised the power of y . how many intiger x satisfied the equation(x^2-x-1)^(x+2)= 1?

• there will be 4 solutions 0,-1,2,-2.
• 10 years agoHelpfull: Yes(35) No(0)
• (x^2-x-1)^(x+2) can only be one when
  x^2-x-1=1 or x+2=0(anything raised to power 0 is 1)
  two solutions for x^2-x-1=1 (x=-1,2)
  and one solution for x+2=0 (x=-2)
  so total possible solution are 3.
• 10 years agoHelpfull: Yes(14) No(19)
• (X^2-X-1)^(X+2)=1
  (4^2-4-1)^(4+2)=1
  (16-4-1)^(6)=1
  (11)^6=1
  SO,THAT 11^6 IS UNIT DIGITS 1
  ANSWER IS 4
• 10 years agoHelpfull: Yes(12) No(9)
• ans)=>3
  1 , -1 and-2
  2-x-1=0
  x=1 or -1
  x+2=0
  x=-2
  
• 10 years agoHelpfull: Yes(3) No(5)
• 3
  (X^2-x-1)^x+2=(1)^0
  (X^2-x-1)=1
  X+2=0
  then x=-1,2,-2
  So 3 solutions
• 10 years agoHelpfull: Yes(2) No(4)
• x would be 2
• 10 years agoHelpfull: Yes(0) No(3)
• x+2=0;
  x=-2;
  x^2-x-1=0;
  x=-1,2;
  total three value;
  
  
• 9 years agoHelpfull: Yes(0) No(1)
• Ans is 4
  
  let x^2-x-1=a and x+2=b
  acc to this question (x^2-x-1)^(x+2)= 1 i.e., a^b = 1 when
  1.) a=1
  2.) b=0, or
  3.) a=-1 and b can be any even integer(2,4,6,....)
  
  1.) x^2-x-1 = 1 => x^2-x-2=0 => (x+1)(x-2) => x = (-1, 2)
  
  2.) x+2=0 => x = -2
  
  3.) x^2-x-1 = -1 => x^2-x = 0 => x = (0, -1)
  
  therefore x = (-2, -1, 0, -1)
• 9 years agoHelpfull: Yes(0) No(1)
• Ans is 4.
  As solutions 0,-1,2,-2
• 8 years agoHelpfull: Yes(0) No(0)
• Ans is 5 (not in the options)
  
  let x^2-x-1=a and x+2=b
  acc to this question (x^2-x-1)^(x+2)= 1 i.e., a^b = 1 when
  1.) a=1
  2.) b=0, or
  3.) a=-1 and b can be any even integer(2,4,6,....)
  
  1.) x^2-x-1 = 1 => x^2-x-2=0 => (x+1)(x-2) => x = (-1, 2)
  
  2.) x+2=0 => x = -2
  
  3.) x^2-x-1 = -1 => x^2-x = 0 => x = (0, -1)
  
  therefore x = (-2, -1, 0, 1,2)
• 7 years agoHelpfull: Yes(0) No(0)
• (X^2-X-1)^(x+2)=1
  (x+2)log(x^2-x-1)=0
  x=-2 is one solution. Other possibility is
  log(x^2-x-1)=0
  x^2-x-1=0. From here we get two integral solutions x=-1,2
  total 3 solution till now
  now taking log on (x^2-x-1) we assumed (x^2-x-1)>0 but (x^2-x-1) may be negative
  thus we solve the inequality:
  (x^2-x-1)
• 7 years agoHelpfull: Yes(0) No(0)