Find the value of b-c if a^3 =b^2, c^2 =d and d-a=5, where a,b,c,d are positive integers.
Answers
Answered by
1
Answer:
Solution
We have,
a
5
=b
4
and c
3
=d
2
a and c are perfect squares.
As c−a=19, a is perfect 4
th
degree integer.
Only possible solutions are
(a,c)=(81,100)
Then,
b=(a
5
)
4
1
=(81
5
)
4
1
={[(3
4
)]
5
}
4
1
=243
And
d=(c
3
)
2
1
=(100
3
)
2
1
=1000
So,
d−b=1000−243
=757
Hence, this is the answer.
Similar questions