Analysis: According to the meaning of the question, m≠0, and m>0 Solution ①: The original equation can be changed to: √[(7m^2+13)+9m]+√[(7m^2+13)-5m]=7m order 7m^2+13=a（a≥13）∴√（a+9m）+√（a-5m）=7m∴√（a+9m）=7m-√（a-5m）a+9m=49m^ 2+a-5m-14m√（a-5m）4

Analysis: According to the meaning of the question, m≠0, and m0

Solution ①: The original equation can be changed to:

√[(7m^2+13)+9m]+√[(7m^2+13)-5m]=7m

order 7m^2+13=a（a≥13）

∴√（a+9m）+√（a-5m）=7m

∴√（a+9m）=7m-√（a-5m）

a+9m=49m ^2+a-5m-14m√（a-5m）

49m^2-14m=14m√（a-5m）

∵m≠0

∴7m-2=2√（a-5m）

∴49m^2- 28m+4=4a-20m

∴4a=49m^2-8m+4

∴4 (7m^2+13)=49m^2-8m+4

∴21m^2-8m-48m=0

∴m 1=（4+ 4√37)/21, m2= (4-4√37)/21 (∵m0, ∴ discard)

∴The solution of the original equation is: m= (4+4√37)/21

Solution ②: Let √ (7m^2+9m+13)=a (a≥0),√(7m^2-5m+13)=b

∴a+b=7m…①

and a^2-b^2=14m

(a+ b) (a-b) = 14m...②

Substituting ① into ②, we get:

a-b=2...③

①+③: 2a=7m+2

∴2√ (7m^2+9m+13)=7m+2

∴28m ^2+36m+52=49m^2+28m+4

∴21m^2-8m-48m=0

∴m1=（4+4√37）/21，m2=（4-4√37）/21（∵ m0, ∴ discarded)

∴The solution of the original equation is: m=(4+4√37)/21

Solution ③: Let the original equation be ① formula

∴7m[√(7m^2+9m+13)-√ (7m^2-5m+13)=14m

∵m≠0

∴√ (7m^2+9m+13)-√ (7m^2-5m+13)=2…②

①+② Got: 2√ (7m^ 2+9m+13)=7m+2

∴28m^2+36m+52=49m^2+28m+4

∴21m^2-8m-48=0

∴m1=（4+4√37）/21,m2 = (4-4√37)/21 (∵m0, ∴ discard)

∴The solution of the original equation is: m= (4+4√37)/21