Given a and b are two natural numbers.
Calculate
kvnmurty:
Use simple algebra. No guessing numbers
Plz Reconsider the Question....
use factorization
Answers
Answered by
1
Heya User,
[tex] \frac{290}{ab} - \frac{3}{b} - \frac{5}{a} = 1 \\\\ =\ \textgreater \ \frac{290}{ab} = \frac{3}{b} + \frac{5}{a} +1\\\\ =\ \textgreater \ \frac{290}{ab} = \frac{3a + 5b + ab}{ab} \\\\ =\ \textgreater \ ab \:[\: 3a + 5b + ab - 290 \:][/tex]
Now, ab ≠ 0;
=> [tex]3a + 5b +ab - 290 = 0\\giving \: us:-\ \textgreater \ \\ 3a + 5b +ab = 290;[/tex]
We know that (a,b) > 0;
--> a[ b + 3 ] + 5[ b + 3 ] = 290 + 15 ----> (i)
=> [ a + 5 ][ b + 3 ] = 305
--> Factors of 305 --> 1*305, 5*61
--> Only possible comparison is :->
--> [ a + 5 ] = 61 => a = 56
--> [ b + 3 ] = 5 ==> b = 2;
Hence, [ (a+b) , (a/b) ] = (58,28) <--- Ans.... :)
[tex] \frac{290}{ab} - \frac{3}{b} - \frac{5}{a} = 1 \\\\ =\ \textgreater \ \frac{290}{ab} = \frac{3}{b} + \frac{5}{a} +1\\\\ =\ \textgreater \ \frac{290}{ab} = \frac{3a + 5b + ab}{ab} \\\\ =\ \textgreater \ ab \:[\: 3a + 5b + ab - 290 \:][/tex]
Now, ab ≠ 0;
=> [tex]3a + 5b +ab - 290 = 0\\giving \: us:-\ \textgreater \ \\ 3a + 5b +ab = 290;[/tex]
We know that (a,b) > 0;
--> a[ b + 3 ] + 5[ b + 3 ] = 290 + 15 ----> (i)
=> [ a + 5 ][ b + 3 ] = 305
--> Factors of 305 --> 1*305, 5*61
--> Only possible comparison is :->
--> [ a + 5 ] = 61 => a = 56
--> [ b + 3 ] = 5 ==> b = 2;
Hence, [ (a+b) , (a/b) ] = (58,28) <--- Ans.... :)
but you tried sincerely. very good. Good attempt. thank you
No pair of such Natural no.s that satisfy the Eqn.
Consider 10th last line...
you did good. but you made a small mistake. . instead of 5b you wrote 4b. that is the reason you couldn't get right answer.
Check your 4 th step. from top. That's the mistake
use factorization
oops
Np .. you now know how to solve it
correct it now. you can EDIT now.
you hav done well.
Answered by
1
290/ab - 3/b - 5/a = 1
→ 290/ab = 3/b + 5/a + 1
→ 290/ab = (3a+5b+ab)/ab
→ 290 = 3a+5b+ab
adding 15 on both sides -
290+15 = 3a+5b+ab+15
→ 305 = a(3+b)+5(3+b)
→ 305 = (a+5)(3+b)
Now we can express 305 as 61×5
→ 61×5 = (a+5)(3+b)
On comparing both sides , we get-
a+5 = 61
→ a = 56
3+b = 5
→ b =2
Now a+b = 56+2 = 58
a/b = 56/2 = 28
___________________________________
→ 290/ab = 3/b + 5/a + 1
→ 290/ab = (3a+5b+ab)/ab
→ 290 = 3a+5b+ab
adding 15 on both sides -
290+15 = 3a+5b+ab+15
→ 305 = a(3+b)+5(3+b)
→ 305 = (a+5)(3+b)
Now we can express 305 as 61×5
→ 61×5 = (a+5)(3+b)
On comparing both sides , we get-
a+5 = 61
→ a = 56
3+b = 5
→ b =2
Now a+b = 56+2 = 58
a/b = 56/2 = 28
___________________________________
thanks
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