a^2-b^4=2009 ,find a+b
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a^2_b^2=2009
a+b(a-b)=2009
a+b=2009÷a-b
a+b(a-b)=2009
a+b=2009÷a-b
aniruddh6:
so the answer is 47
The the answer given in the book is 47
oh sorry
The the answer given in the book is 47
the question is not read with concentration
Answered by
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a²-b⁴=2009
a²-b⁴=(a+b²) (a-b²)
Now, we have to find in factors to 2009
Factors of 2009 are 1,7,41,49,287 and 2009
=(a+b²) (a-b²) =2009
The prime factorization of 2009 is 7²×41
a+b²=x and a-b²=y, then 2b²=x-y
If x=2009,they y=1 and 2b²=2008,
Then b²=2008/2
B=root 1004
X=287,y=7 and 2b²=280
B=root 140
Now,if x=49,y=41 and 2b²=8
Then b²=8/2
b=root 4
b=2
Now putting the value of b=2 in a² - b⁴ =2009
a²-2⁴=2009
a²-16=2009
a²=2009+16
a²=2025
a=root 2025
a=45
So the value of a and b is 45 and 2
a²-b⁴=(a+b²) (a-b²)
Now, we have to find in factors to 2009
Factors of 2009 are 1,7,41,49,287 and 2009
=(a+b²) (a-b²) =2009
The prime factorization of 2009 is 7²×41
a+b²=x and a-b²=y, then 2b²=x-y
If x=2009,they y=1 and 2b²=2008,
Then b²=2008/2
B=root 1004
X=287,y=7 and 2b²=280
B=root 140
Now,if x=49,y=41 and 2b²=8
Then b²=8/2
b=root 4
b=2
Now putting the value of b=2 in a² - b⁴ =2009
a²-2⁴=2009
a²-16=2009
a²=2009+16
a²=2025
a=root 2025
a=45
So the value of a and b is 45 and 2
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