+91-87964 74404
FlagBACK
Question icon
Grade 9Algebra

Can someone explain how to solve this? If a and b are positive integers, and a + b = a/b + b/a, find the value of a^2+b^2?
The answer is 2.

Profile image of Raghav
9 Years agoGrade 9
Answers icon

1 Answer

Profile image of Tanishq Chourishi
9 Years ago
as we rearrange the given equation we get (a+b)ab=a2+b2
====>
a2b=b2a=a2+b2
a2(b-1)+b2(a-1)=0  now as its given a and b are positive integers they can also be called as natural numbers...i.e 1,2,3 ,4.....
therefore a-1 willbe greter than equal to 0 
simmilar for b-1...
now let a2(b-1)=x   ;b2(a-1)=y
now our derived equation says that x + y =zero.. where x,y>=0
 
 which is only possible when x=y=0
 thus from a2(b-1) =0  ==>a=0 or b=1
         from b2(a-1)=0  ==>b=0 or a=1
by  taking the common solution from the above satementswe get a=b=1
 
thus a2+b2=1+1=2.......
   

Other Related Questions on algebra

question mark
What is a binomial expression?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
Can we divide two vectors? If this is possible then how?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
How do you write “the product of 18 and q” as an algebraic expression?
algebra
1 Answer Available

Last Activity: 2 Years ago

question mark
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
algebra
1 Answer Available

Last Activity: 3 Years ago

question mark
Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?
algebra
1 Answer Available

Last Activity: 3 Years ago