Q. If a+b=3, a^2+b^2=7 find a^4+b^4=?

• (1) (a+b)^2=a^2+b^2+2ab
  (3)^2 =(7) +2ab
  2ab =2
  a =1/b
  (2) (a^2+b^2)^2 =a^4+b^4 +2*a^2*b^2
  (7)^2 =a^4+b^4 +2*a^2*(1/a^2) (cause:a =1/b )
  49 =a^4+b^4 +2
  a^4+b^4 =47
  
  so answer is 47.
• 11 years agoHelpfull: Yes(20) No(0)
• 47... square the second one we get a^4+b^4+2a^2b^2=49...(1) similarly square the fist one and we get a^2+b^2+2ab=9 from this we can find out ab value.. and sub this value in equation (1) we get the ans..
• 11 years agoHelpfull: Yes(3) No(0)
• Ans: 47
  a+b=3
  squaring on both the sides
  a^2+b^2+2ab=9
  7+2ab=9 (given a^2+b^2=7)
  ab=1 ->equation 1
  a^2+b^2=7 (given)
  squaring on both the sides,
  a^4+b^4+2a^2b^2=49
  a^4+b^4+2=49 (since, ab=1 (from equation 1)-> a^2b^2=1)
  a^4+b^4=47
• 11 years agoHelpfull: Yes(2) No(0)
• (a+b)^2=a^2+b^2+2ab
  (3)^2 =(7) +2ab
  2ab =2
  a =1/b
  
  
  (a^2+b^2)^2 =a^4+b^4 +2*a^2*b^2
  (7)^2 =a^4+b^4 +2*a^2*(1/a^2) (cause:a =1/b )
  49 =a^4+b^4 +2
  a^4+b^4 =47
  
  
  so answer is 47.
• 11 years agoHelpfull: Yes(2) No(0)
• a^2+b^2=(a+b)^2-2ab
  =>7=3^2-2ab
  =>2ab=2
  =>ab=1.
  Similarly a^4+b^4= (a^2+b^2)^2-2(a^2*b^2)
  =>a^4+b^4=7^2-2(1^2)
  =>a^4+b^4=47
  So answer is 47.
• 11 years agoHelpfull: Yes(2) No(0)
• Answer: 47
  a+b=3, a^2+b^2=7 so, 2ab=(a+b)^2-a^2+b^2
  =9-7
  =2
  =>ab=2/2=1
  (a^4+b^4)=(a^2+b^2)^2-2*a^2*b^2
  =49-2*1
  =47
  
• 11 years agoHelpfull: Yes(1) No(0)
• (a+b)^2 = a^2+b^2+2ab
  => 9=7+2ab
  => ab=1
  (a^2+b^2)^2=a^4+a^4+2a^2b^2
  49=a^4+b^4+2*1
  a^4+b^4=47
• 11 years agoHelpfull: Yes(1) No(1)
• ans :47
  (a+b)^4=a^4+b^4+2*a^2*b^2+2*(a^2+b^2)*(2*a*b)
• 11 years agoHelpfull: Yes(0) No(1)
• (a+b)^2=a^2+b^2+2ab
  9=7+2ab,ab=1,b=1/a
  (a^2+b^2)^2=a^4+b^4+2a^2b^2
  49=a^4+b^4+2a^2*1/a^2=a^4+b^4+2
  49-2=a^4+b^4
  so a^4+b^4=47
• 11 years agoHelpfull: Yes(0) No(0)
• 2ab=(a+b)^2-(a^2+b^2)=9-7=2 then ab=1
  a^4+b^4=(a^2+b^2)^2-2(ab)^2=47
• 11 years agoHelpfull: Yes(0) No(0)
• (a+b)^2=a^2+b^2+2ab
  ==> 2ab= 9-7
  ==> ab=1
  if a^2=m, b^2=n
  (m+n)^2=m^2+n^2+2mn
  ==> 7^2=m^2+n^2+2
  ==> a^4+b^4= 47
• 11 years agoHelpfull: Yes(0) No(0)
• 48
  find a^4+b^4 from (a^2+b^2)^2..
• 11 years agoHelpfull: Yes(0) No(1)
• (a^2+b^2)^2=a^4+b^4+2*(ab)*(ab).......equ-(1)
  ab=[(a+b)^2-(a^2+b^2)]/2
  =>ab=[3^2-7]/2
  =>ab=2/2=1
  put in equ-(1)
  =>(7)^2=a^4+b^4+2*(1)*(1)
  =>49=a^4+b^4+2
  =>a^4+b^4=49-2=47......Answer
• 11 years agoHelpfull: Yes(0) No(0)
• A+B=3
  (A+B)^2=9
  2AB=2
  AB=1
  LET, A^2=X,B^2=Y
  (X+Y)^2=49
  A^4+B^4=47
• 11 years agoHelpfull: Yes(0) No(0)
• (a+b)^2=a^2+b^2+2ab
  9=7+2ab
  ab=1---(1)
  (a^2+b^2)^2=a^4+b^4+2a^2b^2
  49=a^4+b^4+2
  a^4+b^4=47
  
• 11 years agoHelpfull: Yes(0) No(0)
• 49-2=47...
• 11 years agoHelpfull: Yes(0) No(0)
• (a^2+b^2)^2=a^4+b^4+2(ab)^2
  49=a^4+b^4+2
  a^4+b^4=47
  ans 47
• 11 years agoHelpfull: Yes(0) No(0)
• (a+b)=3
  (a+b)^2=9=a^2+b^2+2ab
  ab=1
  (a^2+b^2)(a^2+b^2)=a^4+b^4+2(ab)^2
  a^4+b^4=47
• 11 years agoHelpfull: Yes(0) No(0)
• (a+b)=3--- (i) & a^2+b^2=7----(ii)
  (a+b)^2=9
  a^2+b^2+2ab=9 (sub (ii))
  7+2ab=9
  2ab=2
  ab=1 ---- (iii)
  
  squaring (i)
  (a^2+b^2)^2=49
  a^4+b^4+2a^2b^2=49
  a^4+b^4+2(1)^2=49 (sub (iii))
  a^4+b^4=47
  
  Ans=47
• 11 years agoHelpfull: Yes(0) No(0)
• ans is 47.
  =>a^2+b^2+2ab=(a+b)(a+b)
  =>7+2ab=9 =>ab=1
  =>(a^2+b^2)^2=a^4+b^4+2a^2b^2
  =>49=a^4+b^4=2
  =>a^4+b^4=47.
• 10 years agoHelpfull: Yes(0) No(0)