(a-b)^2=25 and (a+b)^2=1,what is the value of a and b?
a)if a>0>b
b)a=2

• after solving both eqq we get ab= -6
  now from (2) we clearly get the value of (a,b)=(2,-3)
  
  but from (1) ab= -6
  (a,b)=(2,-3)/ (3,-2)
  there are two possible set from statement (1).
  therefore i think only statement 2 is required to ans.
• 10 years agoHelpfull: Yes(14) No(11)
• both statements are required
  
• 10 years agoHelpfull: Yes(5) No(5)
• only (b) can give answer.
  
  By solving these 2 equations we get values of {a,b} as {3,-2} or {-3,2} or {2,-3} or {-2,3}
  
  from (a) we get the values for {a,b} as {3,-2} or {2,-3} , we didn't get single value for a or b thus we cannot answer what is the exact value of a or b.
  
  from (b) we get {a,b}={2,-3}, thus we get values of a and b from condition (b) only.
• 10 years agoHelpfull: Yes(3) No(0)
• both alone csn give the answer
  
  (a-b)^2=a^2+b^2-2ab=25-----(1)
  (a+b)^2=a^2+b^2+2ab=1-----(2)
  
  (1)+(2)
  2(a^2+b^2)=26
  so there are 4 no ( +2,-2,-3,+3)
  
• 10 years agoHelpfull: Yes(2) No(8)
• Either of statements is sufficient.
  (a-b)^2=25 means (a-b)=+5 or -5 and (a+b)^2=1 means (a+b)=+1 or -1..but acc to first statement (a-b)=5 and a-b=-1 are only possible values so by solving,a=2 and b=-3..
  And acc to statement 2nd a=2 is given already. So either of the statements is sufficient.
• 10 years agoHelpfull: Yes(2) No(0)
• it would be better if u will finalise one solution after discussion for any question....
• 9 years agoHelpfull: Yes(2) No(0)
• (a-b)^2=25 and (a+b)^2=1
  a-b=5----------(1)
  a-b=-5---------(2)
  a+b=1 ---------(3)
  a+b=-1 --------(4)
  a)a>0, b
• 10 years agoHelpfull: Yes(1) No(4)
• Here after making a square root then we get a+b=+1 or -1 & a-b=+5 or -5.
  by solving these two equations we get a=-3,2 & b=2,-3.
  So as per given condition if a=2, then b must be -3.
• 10 years agoHelpfull: Yes(1) No(3)
• both alone csn give the answer
  
  (a-b)^2=a^2+b^2-2ab=25-----(1)
  (a+b)^2=a^2+b^2+2ab=1-----(2)
  
  (1)+(2)
  2(a^2+b^2)=26
  a^2+b^2=13
  
  put a=2 ucan easily find b
  so b alone is sufficient to give answer
  
• 10 years agoHelpfull: Yes(1) No(0)
• (a-b)^2=25
  then a-b=+5
  and a-b=-5
  so that
  (a+b)=1
  then
  a+b=+1
  and
  a-b=-1
  we take
  a+b=-1
  a-b=5
  and solve it
  we find the solution
  a=2
  b=-3
  satisfy the condition given in question
  
  
  
• 9 years agoHelpfull: Yes(1) No(0)
• a^2+b^2-2ab=25
  a^2+b^2+2ab=1
  
  subtracting both equation
  -4ab=24
  ab=-6
  a=2
  b=-3
• 10 years agoHelpfull: Yes(0) No(5)
• (a-b)^2=25 and (a+b)^2=1
  a-b=5----------(1)
  a-b=-5---------(2)
  a+b=1 ---------(3)
  a+b=-1 --------(4)
  a)a>0, b
• 10 years agoHelpfull: Yes(0) No(3)
• Ans should be statement b, a=2
  because if we solve the equation then we will get ab= -6,
  now from statement a) we will get only range of value of a and b which will not give exact solution but
  from statement b. we have exact value of a=2 from their we can get value of b easily and we can proof sat a) also.
  but here we need only value of a and b so Statement b is sufficient to give answer.
• 10 years agoHelpfull: Yes(0) No(0)
• Ans: Statement I
  Sol : after solving above equation ,we get
  four combination value for (a,b)
  (2,3),(-2,3),(2,-3)and(-2,-3)
  According condition I , we got
  (2,-3)
  
• 9 years agoHelpfull: Yes(0) No(0)
• (a-b)^2= a^2 + b^2 -2ab = 25 ------1
  (a+b)^2=a^2 + b^2 +2ab = 1 ------2
  
  now sove the equation we got 2(a^2 + b^2)=26
  
  a^2 + b^2= 13
  a and b= 2 or 3
  2^2 + 3^2= 13
  4+9=13
  or a and b -2 or -3
  so both are correct any one are ok for ans
  
• 8 years agoHelpfull: Yes(0) No(0)
• a+b=+1,-1------(1)
  a-b=+5,-5-------(2)
  by solving both 1 & 2 we get
  a= +3,-3 and b=+2,-2
  so its satisfy to the 1 st option in the question "a)if a>0>b"
  so ans is "a"
  
  
  
• 8 years agoHelpfull: Yes(0) No(0)
• Ans : using state I alone we can answer this question but using statement II alone ,
  
  Solution:
  
  using statement I
  
  (a-b)^2=5; (a+b)^2=1
  
  (a-b)=+ 5 or (a-b)= -5;
  
  similarly (a+b)=+1 or (a+b)= -1
  
  Solve the above equations..
  
  since a >0>b the value of a and b should be greater than 0
  hence we get definite value for a and b by using this statement ie a=3 , b=2
  
  USING STATEMENT II
  (a-b)^2=25
  (a+b)^2=1
  
  a^2+b^2-2ab=25
  a^2+b^2+2ab=1
  
  2(a^2+b^2)=26
  a^2+b^2=13
  
  substituting a=2
  2^2+b^2=13
  4+b^2=13
  
  b^2=9
  b=+ 3 or -3
  
  here we do not get definite value of b , it could be 3 or -3 , so cannot be determined using statement II
  
  
  
• 8 years agoHelpfull: Yes(0) No(0)