Question

how many pairs of natural numbers are there the difference of whose squares is 45?

Answer 1

\(a^2-b^2=45\)
hmm lets see

Answer 2

x^2-y^2=45

Answer 3

(x+y)(x-y)=45

Answer 4

ohhh lol
its hyperbola

Answer 5

now possible factors of 45 are 1,3,5,9,15

Answer 6

9 and 6
7 and 2
or 22 and 23 are such numbers only

Answer 7

so only 3 are there

Answer 8

ok ,but is there algebraic way to solve it ? other than trial an error

Answer 9

its not trial its algebraic already

Answer 10

a^2 -b^2 = 45

(a+b)(a-b) = 45

45 = 45*1 or 9*5 or 15*3

if a+b =45
and a-b = 1
a = 23 and b = 22

if a+b = 9
and a-b = 5
a = 7 and b = 2

if a+b =15 and
a-b = 3
a= 9 and b = 6

Answer 11

@gorv how did u find them

Answer 12

this the possible solution and we are considering each one by one

Answer 13

its not trial and error

Answer 14

(x+y)(x-y)=45
means 45 is multiplication of two numbers x+y and x-y
that means its factor needs to be put in such way that they give product of 45