Let this side be AB and the length be √7? . As shown in the figure, the length, width and height from the diagonal of the cube to AB are m, n and h respectively.

According to the meaning of the question:

m & ampsup2= 7-a & amp； sup2

n & ampsup2=? 7-6= 1

h & ampsup2=? 7-b & amp； sup2

By the fact that the square of the diagonal of a cuboid is equal to the sum of the squares of length, width and height, we get

m & ampsup2+n & amp； sup2+h & amp； sup2=(√7)& amp； sup2

Namely:? 15-a & amp； sup2-b & amp； sup2=7

a & ampsup2+b & amp； sup2=8

So there is, (a+b)&; sup2≤? 2(a & amp； sup2+b & amp； sup2)? =? 16

Deduction: a+b≤4

Choose c as the positive solution.