Find the value of a3 + b3.
1. a2+b2 = 13 , a+b=6
2. ab=20 a+b =9

Option:
A.If one alone can give the answer but other can not give answer.
B.If both together can give the answer.
C.If either of two can give the answer
D.Neither of two can give the answer.

• C. Either of the two can give the answer. (But ya the answers are different though).
  
  Using 1)
  a^2+b^2=13
  Now, a+b=6
  or, a^2 + b^2 +2ab = 36
  or, 13 + 2ab = 36
  or, ab=23/2
  
  Thus, a^3 + b^3 = (a+b)(a^2 - ab + b^2) = 9
  
  Using 2)
  (a+b)^2=81
  or, a^2 + b^2 + 2(20)=81
  we get, a^2 + b^2 = 41
  
  Thus, a^3+b^3=(a+b)(a^2 - ab + b^2)= 189.
  
  
• 10 years agoHelpfull: Yes(51) No(0)
• C... coz a3+b3= (a+b)(a2+b2+2ab)
  from 1 and 2 both we can get all the reqd values , using : (a+b)^2= a2+b2+2ab, ie value of ab can be obtained using this identity
• 10 years agoHelpfull: Yes(8) No(6)
• ANSWER==> A
  because 1 has no solution
  for 2 we find a=4 , b=5 or vice-versa
• 10 years agoHelpfull: Yes(4) No(16)
• a3+b3=(a+b)3-3ab(a+b)
  
• 10 years agoHelpfull: Yes(3) No(1)
• ans is (B)because the a3+b3 formula needs to all the above value.
  
• 10 years agoHelpfull: Yes(2) No(10)
• Both of the questions can give the answer. We have the formula a^3-b^3 = (a+b)(a^2+b^2-ab) we can calculate it's value separately by both the statements.so answer is C.
  
  
  @PRANOY BEJ- your answer is wrong as in cube roots of one x^3-1=0 we have roots 1,omega,omega^2, but multiplication of omega && omega^2 =1. In the same way as u are solving may be roots are imaginry but there product can be calculated :)
• 10 years agoHelpfull: Yes(2) No(0)
• C
  a^3+b^3=(a+b)(a^2+ab+b^2)
  using 1
  ab=((a+b)^2-(a^2+b^2)}/2;
  using 2
  a^3+b^3=(a+b)[(a+b)^2-ab]
• 10 years agoHelpfull: Yes(2) No(0)
• answer will be C....both statement can give the values..answers are different coz values of a+b are different in both the statements
• 10 years agoHelpfull: Yes(2) No(1)
• Answer will be option c because using either statements we can directly find the value of a and be.
• 10 years agoHelpfull: Yes(2) No(0)
• Either of them can give the answer.
  a^3+b3=(a+b)(a^2 +b2 -ab)
  ..put the values from any of them in the eqn
• 10 years agoHelpfull: Yes(1) No(0)
• Use formula: a3 + b3 = (a + b)(a2 – ab + b2)
  we have given, 1. a2 + b2= 13 , a+b= 6 and also in 2. ab = 20, a+b=9
  From the first we have found ab = 23/2
  & from the second we can find a2 + b2 = 41
  Now put in the formula we get it as 189 :)
• 9 years agoHelpfull: Yes(1) No(0)
• how can the ans be C,we get different solutions for different options .so that if one alone can give answer the other cannot .Thus it should be A
• 10 years agoHelpfull: Yes(0) No(0)
• Both of the questions can give the answer.
• 2 years agoHelpfull: Yes(0) No(0)