Respuesta :
The value of x is 675 when the a<b<c<d<e are consecutive positive integers such that is a perfect square and a+b+c+d+e is a perfect cube.
Given that,
If a<b<c<d<e are consecutive positive integers such that is a perfect square and a+b+c+d+e is a perfect cube.
We have to find what is the smallest possible value of c.
We know that,
Let b,c,d and e equal to a+1,a+2,a+3, and a+4 respectively.
Let the square and cube be k² and m³ where both k and m are integers.
Then 5a+10=m³
Now, we know m³ is a multiple of 125 and m is a multiple of 5.
The lower is m, the lower the value of c will be.
Start from 5 and add 5 to each time.
m=5 gives no solution for k.
m=10 gives no solution for k.
m=15 gives no solution for k.
10+5a=15³
2+a=675
c=675
Therefore, The value of x is 675 when the a<b<c<d<e are consecutive positive integers such that is a perfect square and a+b+c+d+e is a perfect cube.
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